Answer:
2:7
Step-by-step explanation:
4+10=14
The least common factor is 2.
4/2=2
14/2=7
Answer:
A. sec =12/13×
B. COS =12/13×
C. tan =12/5✓
D. sin =12/13 ✓
Step-by-step explanation:
we know,
using Pythagoras formula,
p=12,h=13 ,b=?
h^2 =p^2 +b^2
b=5
so tan = p/b
=12/5
sin=p/h and cosec= h/p
D. sin =12/13
Step-by-step explanation:
![\bf \underline{➤ Answer\: (1)-} \\](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cunderline%7B%E2%9E%A4%20%20Answer%5C%3A%20%281%29-%7D%20%5C%5C%20)
![{\tt \longrightarrow \dfrac{{2}^{3} \times {3}^{4} \times 4}{3 \times 32}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%5Cdfrac%7B%7B2%7D%5E%7B3%7D%20%5Ctimes%20%7B3%7D%5E%7B4%7D%20%5Ctimes%204%7D%7B3%20%5Ctimes%2032%7D%7D)
Convert all of them into exponents and powers form.
![{\tt \longrightarrow \dfrac{{2}^{3} \times {3}^{4} \times {2}^{2}}{{3}^{1} \times {2}^{5}}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%5Cdfrac%7B%7B2%7D%5E%7B3%7D%20%5Ctimes%20%7B3%7D%5E%7B4%7D%20%5Ctimes%20%7B2%7D%5E%7B2%7D%7D%7B%7B3%7D%5E%7B1%7D%20%5Ctimes%20%7B2%7D%5E%7B5%7D%7D%7D)
Simplify each of them...
![{\tt \longrightarrow \dfrac{{2}^{3 + 2} \times {3}^{4}}{{3}^{1} \times {2}^{5}} = \dfrac{{2}^{5} \times {3}^{4}}{{3}^{1} \times {2}^{5}}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%5Cdfrac%7B%7B2%7D%5E%7B3%20%2B%202%7D%20%5Ctimes%20%7B3%7D%5E%7B4%7D%7D%7B%7B3%7D%5E%7B1%7D%20%5Ctimes%20%7B2%7D%5E%7B5%7D%7D%20%3D%20%5Cdfrac%7B%7B2%7D%5E%7B5%7D%20%5Ctimes%20%7B3%7D%5E%7B4%7D%7D%7B%7B3%7D%5E%7B1%7D%20%5Ctimes%20%7B2%7D%5E%7B5%7D%7D%7D)
![{\tt \longrightarrow {2}^{5 - 5} \times {3}^{4 - 1} = {2}^{0} \times {3}^{3}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%7B2%7D%5E%7B5%20-%205%7D%20%5Ctimes%20%7B3%7D%5E%7B4%20-%201%7D%20%3D%20%7B2%7D%5E%7B0%7D%20%5Ctimes%20%7B3%7D%5E%7B3%7D%7D%20)
![\bf \underline{➤ Answer\: (2)-} \\](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cunderline%7B%E2%9E%A4%20%20Answer%5C%3A%20%282%29-%7D%20%5C%5C%20)
![{\tt \longrightarrow \bigg(( {5}^{2} {)}^{3} \times {5}^{4} \bigg) \div {5}^{7}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%5Cbigg%28%28%20%7B5%7D%5E%7B2%7D%20%7B%29%7D%5E%7B3%7D%20%5Ctimes%20%7B5%7D%5E%7B4%7D%20%5Cbigg%29%20%5Cdiv%20%7B5%7D%5E%7B7%7D%7D%20)
![{\tt \longrightarrow \bigg({5}^{2 \times 3}\times {5}^{4} \bigg) \div {5}^{7}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%5Cbigg%28%7B5%7D%5E%7B2%20%5Ctimes%203%7D%5Ctimes%20%7B5%7D%5E%7B4%7D%20%5Cbigg%29%20%5Cdiv%20%7B5%7D%5E%7B7%7D%7D%20)
![{\tt \longrightarrow {5}^{6 + 4} \div {5}^{7} = {5}^{10} \div {5}^{7}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%7B5%7D%5E%7B6%20%2B%204%7D%20%5Cdiv%20%7B5%7D%5E%7B7%7D%20%3D%20%7B5%7D%5E%7B10%7D%20%5Cdiv%20%7B5%7D%5E%7B7%7D%7D%20)
![{\tt \longrightarrow {5}^{10 - 7}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%7B5%7D%5E%7B10%20-%207%7D%7D)
![\bf \underline{➤ Answer\: (3)-} \\](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cunderline%7B%E2%9E%A4%20%20Answer%5C%3A%20%283%29-%7D%20%5C%5C%20)
![{\tt \longrightarrow {25}^{4} \times {5}^{3}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%7B25%7D%5E%7B4%7D%20%5Ctimes%20%7B5%7D%5E%7B3%7D%7D)
![{\tt \longrightarrow ( {5}^{2})^{4} \times {5}^{3} = {5}^{2 \times 4} \times {5}^{3}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%28%20%7B5%7D%5E%7B2%7D%29%5E%7B4%7D%20%5Ctimes%20%7B5%7D%5E%7B3%7D%20%3D%20%7B5%7D%5E%7B2%20%5Ctimes%204%7D%20%5Ctimes%20%7B5%7D%5E%7B3%7D%7D)
![{\tt \longrightarrow {5}^{8} \times {5}^{3} = {5}^{8 + 3}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%7B5%7D%5E%7B8%7D%20%5Ctimes%20%7B5%7D%5E%7B3%7D%20%3D%20%7B5%7D%5E%7B8%20%2B%203%7D%7D)
![\bf \underline{➤ Answer\: (4)-} \\](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cunderline%7B%E2%9E%A4%20%20Answer%5C%3A%20%284%29-%7D%20%5C%5C%20)
![\tt \longrightarrow \dfrac{3 \times {7}^{2} \times {11}^{8}}{21 \times {11}^{3}}](https://tex.z-dn.net/?f=%5Ctt%20%5Clongrightarrow%20%5Cdfrac%7B3%20%5Ctimes%20%7B7%7D%5E%7B2%7D%20%5Ctimes%20%7B11%7D%5E%7B8%7D%7D%7B21%20%5Ctimes%20%7B11%7D%5E%7B3%7D%7D%20)
![\tt \longrightarrow \dfrac{{3}^{1} \times {7}^{2} \times {11}^{8}}{ {7}^{1} \times {3}^{1} \times {11}^{3}}](https://tex.z-dn.net/?f=%5Ctt%20%5Clongrightarrow%20%5Cdfrac%7B%7B3%7D%5E%7B1%7D%20%5Ctimes%20%7B7%7D%5E%7B2%7D%20%5Ctimes%20%7B11%7D%5E%7B8%7D%7D%7B%20%7B7%7D%5E%7B1%7D%20%5Ctimes%20%7B3%7D%5E%7B1%7D%20%5Ctimes%20%7B11%7D%5E%7B3%7D%7D%20)
![{\tt \longrightarrow {3}^{1 - 1} \times {7}^{2 - 1} \times {11}^{8 - 3}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%7B3%7D%5E%7B1%20-%201%7D%20%5Ctimes%20%7B7%7D%5E%7B2%20-%201%7D%20%5Ctimes%20%7B11%7D%5E%7B8%20-%203%7D%7D)
![{\tt \longrightarrow {7}^{1} \times {11}^{5}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%7B7%7D%5E%7B1%7D%20%5Ctimes%20%7B11%7D%5E%7B5%7D%7D)
![\bf \underline{➤ Answer\: (5)-} \\](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cunderline%7B%E2%9E%A4%20%20Answer%5C%3A%20%285%29-%7D%20%5C%5C%20)
![\tt \longrightarrow \dfrac{{3}^{7}}{ {3}^{4} \times {3}^{3}}](https://tex.z-dn.net/?f=%5Ctt%20%5Clongrightarrow%20%5Cdfrac%7B%7B3%7D%5E%7B7%7D%7D%7B%20%7B3%7D%5E%7B4%7D%20%5Ctimes%20%7B3%7D%5E%7B3%7D%7D%20)
![\tt \longrightarrow \dfrac{{3}^{7}}{ {3}^{4 + 3}} = \dfrac{{3}^{7}}{{3}^{7}}](https://tex.z-dn.net/?f=%5Ctt%20%5Clongrightarrow%20%5Cdfrac%7B%7B3%7D%5E%7B7%7D%7D%7B%20%7B3%7D%5E%7B4%20%2B%203%7D%7D%20%3D%20%5Cdfrac%7B%7B3%7D%5E%7B7%7D%7D%7B%7B3%7D%5E%7B7%7D%7D%20)
![\tt \longrightarrow {3}^{7 - 7}](https://tex.z-dn.net/?f=%5Ctt%20%5Clongrightarrow%20%7B3%7D%5E%7B7%20-%207%7D)
![\tt \longrightarrow {3}^{0}](https://tex.z-dn.net/?f=%5Ctt%20%5Clongrightarrow%20%7B3%7D%5E%7B0%7D)
![\bf \underline{➤ Answer\: (6)-} \\](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cunderline%7B%E2%9E%A4%20%20Answer%5C%3A%20%286%29-%7D%20%5C%5C%20)
![{\tt \longrightarrow {2}^{0} + {3}^{0} + {4}^{0}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%7B2%7D%5E%7B0%7D%20%2B%20%7B3%7D%5E%7B0%7D%20%2B%20%7B4%7D%5E%7B0%7D%7D%20)
![{\tt \longrightarrow 1 + 1 + 1 = 3}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%201%20%2B%201%20%2B%201%20%3D%203%7D%20)
![{\tt \longrightarrow {3}^{1}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%7B3%7D%5E%7B1%7D%7D%20)
![\bf \underline{➤ Answer\: (7)-} \\](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cunderline%7B%E2%9E%A4%20%20Answer%5C%3A%20%287%29-%7D%20%5C%5C%20)
![{\tt \longrightarrow {2}^{0} \times {3}^{0} \times {4}^{0}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%7B2%7D%5E%7B0%7D%20%5Ctimes%20%7B3%7D%5E%7B0%7D%20%5Ctimes%20%7B4%7D%5E%7B0%7D%7D%20)
![{\tt \longrightarrow 1 \times 1 \times 1 = 1}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%201%20%5Ctimes%201%20%5Ctimes%201%20%3D%201%7D%20)
![{\tt \longrightarrow {1}^{1}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%7B1%7D%5E%7B1%7D%7D%20)
![\bf \underline{➤ Answer\: (8)-} \\](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cunderline%7B%E2%9E%A4%20%20Answer%5C%3A%20%288%29-%7D%20%5C%5C%20)
![{\tt \longrightarrow ({3}^{0} + {2}^{0}) \times {5}^{0}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%28%7B3%7D%5E%7B0%7D%20%2B%20%7B2%7D%5E%7B0%7D%29%20%5Ctimes%20%7B5%7D%5E%7B0%7D%7D%20)
![{\tt \longrightarrow (1 + 1) \times 1 = 2 \times 1}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%281%20%2B%201%29%20%5Ctimes%201%20%3D%202%20%5Ctimes%201%7D%20)
![{\tt \longrightarrow {2}^{1}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%7B2%7D%5E%7B1%7D%7D)
![\bf \underline{➤ Answer\: (9)-} \\](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cunderline%7B%E2%9E%A4%20%20Answer%5C%3A%20%289%29-%7D%20%5C%5C%20)
![\tt \longrightarrow \dfrac{{2}^{8} \times {a}^{5}}{{4}^{3} \times {a}^{3}}](https://tex.z-dn.net/?f=%5Ctt%20%5Clongrightarrow%20%5Cdfrac%7B%7B2%7D%5E%7B8%7D%20%5Ctimes%20%7Ba%7D%5E%7B5%7D%7D%7B%7B4%7D%5E%7B3%7D%20%5Ctimes%20%7Ba%7D%5E%7B3%7D%7D%20)
![\tt \longrightarrow \dfrac{{2}^{8} \times {a}^{5}}{( {2}^{2}{)}^{3} \times {a}^{3}}](https://tex.z-dn.net/?f=%5Ctt%20%5Clongrightarrow%20%5Cdfrac%7B%7B2%7D%5E%7B8%7D%20%5Ctimes%20%7Ba%7D%5E%7B5%7D%7D%7B%28%20%7B2%7D%5E%7B2%7D%7B%29%7D%5E%7B3%7D%20%5Ctimes%20%7Ba%7D%5E%7B3%7D%7D%20)
![\tt \longrightarrow \dfrac{{2}^{8} \times {a}^{5}}{{2}^{2 \times 3} \times {a}^{3}} = \dfrac{{2}^{8} \times {a}^{5}}{{2}^{6} \times {a}^{3}}](https://tex.z-dn.net/?f=%5Ctt%20%5Clongrightarrow%20%5Cdfrac%7B%7B2%7D%5E%7B8%7D%20%5Ctimes%20%7Ba%7D%5E%7B5%7D%7D%7B%7B2%7D%5E%7B2%20%5Ctimes%203%7D%20%5Ctimes%20%7Ba%7D%5E%7B3%7D%7D%20%3D%20%5Cdfrac%7B%7B2%7D%5E%7B8%7D%20%5Ctimes%20%7Ba%7D%5E%7B5%7D%7D%7B%7B2%7D%5E%7B6%7D%20%5Ctimes%20%7Ba%7D%5E%7B3%7D%7D%20)
![\tt \longrightarrow {2}^{8 - 6} \times {a}^{5 - 3}](https://tex.z-dn.net/?f=%5Ctt%20%5Clongrightarrow%20%7B2%7D%5E%7B8%20-%206%7D%20%5Ctimes%20%7Ba%7D%5E%7B5%20-%203%7D)
![\tt \longrightarrow {2}^{2} \times {a}^{2}](https://tex.z-dn.net/?f=%5Ctt%20%5Clongrightarrow%20%7B2%7D%5E%7B2%7D%20%5Ctimes%20%7Ba%7D%5E%7B2%7D)
![\bf \underline{➤ Answer\: (10)-} \\](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cunderline%7B%E2%9E%A4%20%20Answer%5C%3A%20%2810%29-%7D%20%5C%5C%20)
![{\tt \longrightarrow \bigg(\dfrac{{a}^{5}}{{a}^{3}} \bigg) \times {a}^{8}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%5Cbigg%28%5Cdfrac%7B%7Ba%7D%5E%7B5%7D%7D%7B%7Ba%7D%5E%7B3%7D%7D%20%5Cbigg%29%20%5Ctimes%20%7Ba%7D%5E%7B8%7D%7D)
![{\tt \longrightarrow {a}^{5 - 3} \times {a}^{8}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%7Ba%7D%5E%7B5%20-%203%7D%20%5Ctimes%20%7Ba%7D%5E%7B8%7D%7D)
![{\tt \longrightarrow {a}^{2} \times {a}^{8} = {a}^{2 + 8}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%7Ba%7D%5E%7B2%7D%20%5Ctimes%20%7Ba%7D%5E%7B8%7D%20%3D%20%7Ba%7D%5E%7B2%20%2B%208%7D%7D)
![{\tt \longrightarrow {a}^{10}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%7Ba%7D%5E%7B10%7D%7D)
![\bf \underline{➤ Answer\: (11)-} \\](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cunderline%7B%E2%9E%A4%20%20Answer%5C%3A%20%2811%29-%7D%20%5C%5C%20)
![{\tt \longrightarrow \dfrac{{4}^{5} \times {a}^{8} \: {b}^{3}}{{4}^{5} \times {a}^{5} \: {b}^{2}}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%5Cdfrac%7B%7B4%7D%5E%7B5%7D%20%5Ctimes%20%7Ba%7D%5E%7B8%7D%20%5C%3A%20%7Bb%7D%5E%7B3%7D%7D%7B%7B4%7D%5E%7B5%7D%20%5Ctimes%20%7Ba%7D%5E%7B5%7D%20%5C%3A%20%7Bb%7D%5E%7B2%7D%7D%7D)
![{\tt \longrightarrow {4}^{5 - 5} \times {a}^{8 - 5} \times {b}^{3 - 2}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%7B4%7D%5E%7B5%20-%205%7D%20%5Ctimes%20%7Ba%7D%5E%7B8%20-%205%7D%20%5Ctimes%20%7Bb%7D%5E%7B3%20-%202%7D%7D)
![{\tt \longrightarrow {4}^{0} \times {a}^{3} \times {b}^{1}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%7B4%7D%5E%7B0%7D%20%5Ctimes%20%7Ba%7D%5E%7B3%7D%20%5Ctimes%20%7Bb%7D%5E%7B1%7D%7D%20)
![{\tt \longrightarrow {a}^{3} \times {b}^{1}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%7Ba%7D%5E%7B3%7D%20%5Ctimes%20%7Bb%7D%5E%7B1%7D%7D%20)
![\bf \underline{➤ Answer\: (12)-} \\](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cunderline%7B%E2%9E%A4%20%20Answer%5C%3A%20%2812%29-%7D%20%5C%5C%20)
![{\tt \longrightarrow \bigg( {2}^{3} \times 2 \bigg)^{2}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%5Cbigg%28%20%7B2%7D%5E%7B3%7D%20%5Ctimes%202%20%5Cbigg%29%5E%7B2%7D%7D)
![{\tt \longrightarrow \bigg( {2}^{3 + 1}\bigg)^{2} = {2}^{4 \times 2}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%5Cbigg%28%20%7B2%7D%5E%7B3%20%2B%201%7D%5Cbigg%29%5E%7B2%7D%20%3D%20%7B2%7D%5E%7B4%20%5Ctimes%202%7D%7D)
![{\tt \longrightarrow {2}^{8}}](https://tex.z-dn.net/?f=%7B%5Ctt%20%5Clongrightarrow%20%7B2%7D%5E%7B8%7D%7D)
━━━━━━━━━━━━━━━━━━━━━
![\bf \underline{Used \:Laws\: of \:Intergal\:Exponents-} \\](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cunderline%7BUsed%20%5C%3ALaws%5C%3A%20of%20%5C%3AIntergal%5C%3AExponents-%7D%20%5C%5C%20)
![{\to \sf {a}^{m} \times {a}^{n} = {a}^{m + n}}](https://tex.z-dn.net/?f=%7B%5Cto%20%5Csf%20%7Ba%7D%5E%7Bm%7D%20%5Ctimes%20%7Ba%7D%5E%7Bn%7D%20%3D%20%7Ba%7D%5E%7Bm%20%2B%20n%7D%7D)
![{\to \sf {a}^{m} \div {a}^{n} = {a}^{m - n}}](https://tex.z-dn.net/?f=%7B%5Cto%20%5Csf%20%7Ba%7D%5E%7Bm%7D%20%5Cdiv%20%7Ba%7D%5E%7Bn%7D%20%3D%20%7Ba%7D%5E%7Bm%20-%20n%7D%7D)
![{\to \sf \bigg( {a}^{m} \bigg)^{n} = {a}^{m \times n}}](https://tex.z-dn.net/?f=%7B%5Cto%20%5Csf%20%5Cbigg%28%20%7Ba%7D%5E%7Bm%7D%20%5Cbigg%29%5E%7Bn%7D%20%3D%20%7Ba%7D%5E%7Bm%20%5Ctimes%20n%7D%7D)
![{\to \sf \dfrac{ {a}^{m}}{ {b}^{m}} = \bigg( {\dfrac{a}{b}}\bigg)^{m}}](https://tex.z-dn.net/?f=%7B%5Cto%20%5Csf%20%5Cdfrac%7B%20%7Ba%7D%5E%7Bm%7D%7D%7B%20%7Bb%7D%5E%7Bm%7D%7D%20%3D%20%5Cbigg%28%20%7B%5Cdfrac%7Ba%7D%7Bb%7D%7D%5Cbigg%29%5E%7Bm%7D%7D)
![{\to \sf {a}^{0} = 1}](https://tex.z-dn.net/?f=%7B%5Cto%20%5Csf%20%7Ba%7D%5E%7B0%7D%20%3D%201%7D)
![{\to \sf {a}^{ - 1} = \dfrac{1}{a}}](https://tex.z-dn.net/?f=%7B%5Cto%20%5Csf%20%7Ba%7D%5E%7B%20-%201%7D%20%3D%20%5Cdfrac%7B1%7D%7Ba%7D%7D)
![\textsf{Hope this helps!!}\\](https://tex.z-dn.net/?f=%5Ctextsf%7BHope%20this%20helps%21%21%7D%5C%5C)
Answer:
![\displaystyle 8,1](https://tex.z-dn.net/?f=%5Cdisplaystyle%208%2C1)
Step-by-step explanation:
Use the Pythagorean Theorem twise [first time for the <em>reflexive </em><em>edge</em> and the second time for the <em>longer leg</em> of the other triangle]:
![\displaystyle a^2 + b^2 = c^2 \\ \\ a^2 + 5^2 = 10^2 \hookrightarrow 100 = 25 + a^2 \hookrightarrow \sqrt{75} = \sqrt{x^2}; 5\sqrt{3}\:[or\:8,6602540378...] = a \\ \\ \\ \\ a^2 + b^2 = c^2 \\ \\ x^2 + 3^2 = 5\sqrt{3}^2 \hookrightarrow 75 = 9 + x^2 \hookrightarrow \sqrt{66} = \sqrt{x^2}; \sqrt{66}\:[or\:8,1240384046...] = x \\ \\ \boxed{\boxed{8,1 \approx x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20a%5E2%20%2B%20b%5E2%20%3D%20c%5E2%20%5C%5C%20%5C%5C%20a%5E2%20%2B%205%5E2%20%3D%2010%5E2%20%5Chookrightarrow%20100%20%3D%2025%20%2B%20a%5E2%20%5Chookrightarrow%20%5Csqrt%7B75%7D%20%3D%20%5Csqrt%7Bx%5E2%7D%3B%205%5Csqrt%7B3%7D%5C%3A%5Bor%5C%3A8%2C6602540378...%5D%20%3D%20a%20%5C%5C%20%5C%5C%20%5C%5C%20%5C%5C%20a%5E2%20%2B%20b%5E2%20%3D%20c%5E2%20%5C%5C%20%5C%5C%20x%5E2%20%2B%203%5E2%20%3D%205%5Csqrt%7B3%7D%5E2%20%5Chookrightarrow%2075%20%3D%209%20%2B%20x%5E2%20%5Chookrightarrow%20%5Csqrt%7B66%7D%20%3D%20%5Csqrt%7Bx%5E2%7D%3B%20%5Csqrt%7B66%7D%5C%3A%5Bor%5C%3A8%2C1240384046...%5D%20%3D%20x%20%5C%5C%20%5C%5C%20%5Cboxed%7B%5Cboxed%7B8%2C1%20%5Capprox%20x%7D%7D)
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