The main rules that we use here are :
i)
![\sqrt{a \cdot b}= \sqrt{a} \cdot \sqrt{b}](https://tex.z-dn.net/?f=%20%5Csqrt%7Ba%20%5Ccdot%20b%7D%3D%20%20%5Csqrt%7Ba%7D%20%5Ccdot%20%5Csqrt%7Bb%7D%20)
for nonnegative values a and b.
ii)
![\sqrt{a} \cdot \sqrt{a} =a](https://tex.z-dn.net/?f=%20%5Csqrt%7Ba%7D%20%5Ccdot%20%20%5Csqrt%7Ba%7D%20%3Da)
.
Thus, first 'decompose' the numbers in the radicals into prime factors:
![4 \sqrt{3} \cdot 10 \cdot \sqrt{2\cdot2\cdot3}\cdot \sqrt{2\cdot 3}\cdot \sqrt{2}.](https://tex.z-dn.net/?f=4%20%5Csqrt%7B3%7D%20%5Ccdot%2010%20%5Ccdot%20%20%5Csqrt%7B2%5Ccdot2%5Ccdot3%7D%5Ccdot%20%20%5Csqrt%7B2%5Ccdot%203%7D%5Ccdot%20%20%5Csqrt%7B2%7D.%20%20%20%20)
.
By rule (i) we write:
![4 \sqrt{3} \cdot 10 \cdot \sqrt{2}\cdot \sqrt{2}\cdot \sqrt{\cdot3}\cdot \sqrt{2} \cdot \sqrt{3} \cdot \sqrt{2}](https://tex.z-dn.net/?f=4%20%5Csqrt%7B3%7D%20%5Ccdot%2010%20%5Ccdot%20%5Csqrt%7B2%7D%5Ccdot%20%5Csqrt%7B2%7D%5Ccdot%20%5Csqrt%7B%5Ccdot3%7D%5Ccdot%20%5Csqrt%7B2%7D%20%5Ccdot%20%20%5Csqrt%7B3%7D%20%5Ccdot%20%5Csqrt%7B2%7D)
.
We can collect these terms as follows:
![40 \sqrt{3}\cdot (\sqrt{3}\cdot \sqrt{3}) \cdot (\sqrt{2}\cdot \sqrt{2}) \cdot( \sqrt{2} \cdot \sqrt{2})](https://tex.z-dn.net/?f=40%20%5Csqrt%7B3%7D%5Ccdot%20%28%5Csqrt%7B3%7D%5Ccdot%20%5Csqrt%7B3%7D%29%20%5Ccdot%20%28%5Csqrt%7B2%7D%5Ccdot%20%5Csqrt%7B2%7D%29%20%5Ccdot%28%20%5Csqrt%7B2%7D%20%5Ccdot%20%5Csqrt%7B2%7D%29)
, and by rule (ii) we have:
![40 \sqrt{3}\cdot 3 \cdot 2 \cdot2=40\cdot12\cdot \sqrt{3}=480 \sqrt{3}.](https://tex.z-dn.net/?f=40%20%5Csqrt%7B3%7D%5Ccdot%203%20%5Ccdot%202%20%5Ccdot2%3D40%5Ccdot12%5Ccdot%20%5Csqrt%7B3%7D%3D480%20%5Csqrt%7B3%7D.)
Answer:
![480 \sqrt{3}](https://tex.z-dn.net/?f=480%20%5Csqrt%7B3%7D%20%20)
.
Answer:
a = 60
b = 90
c = 150
Step-by-step explanation:
Numerele a, b și c sunt direct proporționale cu 2, 3 și 5.
Unde k este constantă de proporționalitate
a ∝ 2
a = 2k
b ∝ 3
b = 3k
c ∝ 5
c = 5k
Dacă media aritmetică a celor trei numere este egală cu 100, determinați numerele a, b și c
= 2k + 3k + 5k / 3 = 100
= 10k / 3 = 100
Cross Multiply
= 10k = 3 × 100
= 10k = 300
Împărțiți ambele părți la 10
k = 300/10
k = 30
Pentru numărul a
a = 2k
a = 2 × 30
a = 60
Pentru numărul b
b = 3k
b = 3 × 30
b = 90
Pentru numărul c
c = 5k
c = 5 × 30
c = 150
Prin urmare, a = 60, b = 90, c = 150
(180-x) + 18 + 30 + x/2 = 180
=> 180 + 48 - x + x/2 = 180
=> -x/2 + 48 = 0
=> x/2 = 48
=> x = 48×2 = 96°
1800 because the 18 cant fit in the tens
Answer:
17.1 cm
Step-by-step explanation:
A screw driver is a mechanical tool or device which is mainly used for screwing the screws and unscrewing them. It is also used for removing the nuts and bolts and also serves a variety of uses.
It is typically made of steel and has a handle and a shaft which ends as a tip.
In the context, the length of the screw driver from the given figure expressed to the nearest tenth of a centimeter is 17.1 cm.
It is also equivalent to
inch.