Question

Please help another assignment I’m not very good at math !!

Answer 1

Answer:

Prime Factorization of 576

$576=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3$

Prime Factorization of 64

$64=2\times 2\times 2\times 2\times 2\times 2$

The Expression in simplest form is

$\sqrt{\dfrac{576}{64} }=\dfrac{3}{1}$

Step-by-step explanation:

Simplify:

$\sqrt{\dfrac{576}{64} }$

Now,

Prime Factorization of 576

$576=2\times 288\\576=2\times 2\times 144\\576=2\times 2\times 2\times 72\\576=2\times 2\times 2\times 2\times 36\\576=2\times 2\times 2\times 2\times 2\times 18\\576=2\times 2\times 2\times 2\times 2\times 2\times 9\\576=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3$

Prime Factorization of 64

$64=2\times 32\\64=2\times 2\times 16\\64=2\times 2\times 2\times 8\\64=2\times 2\times 2\times 2\times 4\\64=2\times 2\times 2\times 2\times 2\times 2$

Now,

$\sqrt{\dfrac{576}{64} }=\sqrt{\dfrac{2\times 2\times 2\times 2\times 2\times 2\times 3\times 3}{2\times 2\times 2\times 2\times 2\times 2} }\\ \sqrt{\dfrac{576}{64} }=\sqrt{\dfrac{3\times 3}{1}}\\\therefore \sqrt{\dfrac{576}{64} }=3$

The Expression in simplest form is

$\sqrt{\dfrac{576}{64} }=\dfrac{3}{1}$