Question

What is the square root of 180x^9y^16 in simplest form?

Answer 1

$\sqrt{180x ^{9y ^{16} } }$

Apply radical  rule :

$\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}$

$\sqrt{180} \sqrt{x ^{9y^{16} } }$

Break  the number  to its primes : $180 : 2^2*3^2*5$

$\sqrt{2^2*3^2*5}$

Apply radical  rule :

$\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}$

$\sqrt{5} \sqrt{2^2} \sqrt{3^2}$

Apply radical  rule :

$\sqrt[n]{a^n} =a$

$\sqrt{2^2} =2$

$2* \sqrt{5} \sqrt{3^2}$

Apply radical  rule :

$\sqrt[n]{a^n} =a$

$\sqrt{3^2} =3$

$= 2*3* \sqrt{5}$

Refine:

$\sqrt{5} *6$

$\sqrt{5} *6 \sqrt{x ^{9y ^{16} } }$

Apply radical rule : 

$\sqrt[n]{a^m} = a \frac{m}{n}$

$\sqrt{x ^{9y ^{16} } } = x \frac{9y ^{16} }{2}$

$= \sqrt{5} *6x \frac{9y ^{16} }{2}$

hope this helps!