Question

Give the whole solution....​

Answer 1

Given:

$\sqrt{\dfrac{8^{10} + 4^{10}}{64^2+4^9 \times 16} }$

To Find:

The simplest form

Solution:

$\sqrt{\dfrac{8^{10} + 4^{10}}{64^2+4^9 \times 16} }$

Rewrite all the numbers to base number of 2:

$= \sqrt{\dfrac{2^{3\times10} + 2^{2\times 10}}{2^{6 \times 2}+2^{2 \times 9} \times 2^4} }$

$= \sqrt{\dfrac{2^{30} + 2^{20}}{2^{12}+2^{18} \times 2^4} }$

Apply: aⁿ  x aˣ = aⁿ⁺ˣ:

 $= \sqrt{\dfrac{2^{30} + 2^{20}}{2^{12}+2^{18 + 4} }$

$= \sqrt{\dfrac{2^{30} + 2^{20}}{2^{12}+2^{22} }$

Take out common terms:

$= \sqrt{\dfrac{2^{20}(2^{10} + 1) }{2^{12}(1+2^{10}) }$

$= \sqrt{\dfrac{2^{20}(2^{10} + 1) }{2^{12}(2^{10} + 1) }$

Simplify by cancelling the same term for numerator and denominator:

$= \sqrt{\dfrac{2^{20} }{2^{12} }$

Apply: aⁿ  ÷ aˣ = aⁿ⁻ˣ:

$= \sqrt{2^{20 - 12} }$

$= \sqrt{2^{8} }$

$= 2^4$

Find the value:

$= 16$