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Anastasy [175]
3 years ago
8

What is sqrt 6/5 in it's simplest radical form?

Mathematics
1 answer:
Tanya [424]3 years ago
8 0
\sqrt{\cfrac{6}{5}}\impliedby \textit{simplified, right?}

for... is more or less simplified, so.. .it can't be simplified any further
if anything at all, it can simply be "rationalized"
namely

\sqrt{\cfrac{6}{5}}\implies \cfrac{\sqrt{6}}{\sqrt{5}}\impliedby \textit{now rationalizing it}
\\ \quad \\
\cfrac{\sqrt{6}}{\sqrt{5}}\cdot \cfrac{\sqrt{5}}{\sqrt{5}}\implies \cfrac{\sqrt{6}\sqrt{5}}{\sqrt{5^2}}\implies \cfrac{\sqrt{30}}{5}
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<img src="https://tex.z-dn.net/?f=4%20%5Ctimes%208%20%5E%7B2x%20%2B%201%3F%7D%20%20%3D%2032%20%5E%7Bx%20%2B%202%7D%20" id="TexFo
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Answer:

x = 5

Step-by-step explanation:

<u>__________________________________________________________</u>

<u>FACTS TO KNOW BEFORE SOLVING</u> :-

  • a^x \times a^y = a^{x+y}
  • In an equation , if the bases are same in both L.H.S. & R.H.S. then , the power of the bases on both the sides of equation should be equal. For e.g. : a^x = a^y  ⇒  x = y  [∵ Bases are equal on both the sides]

<u>__________________________________________________________</u>

4 \times 8^{2x+1} = 32^{x+2}

Lets express it in terms of 2.

=> 2^2 \times 2^{3 (2x+1)} = 2^{5(x+2)}

=> 2^2 \times 2^{6x+3} = 2^{5x+10}

=> 2^{2 + 6x+3} = 2^{5x+10}

=> 2^{6x+5} = 2^{5x+10}

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=> 6x + 5 = 5x + 10

=> 6x - 5x = 10 - 5

=> x = 5

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