Question

Square root of 144 X^7 Y^5

Answer 1

The first step to solving this is to factor out the first perfect square
$\sqrt{12^{2} x^{7} y^{5} }$
now factor out the second perfect square
$\sqrt{ 12^{2} x^{6} X x y^{5} }$
then factor out the second perfect square 
$\sqrt{ 12^{2} x^{6} X x y^{4} X y}$
the root of a product is equal to the product of the roots of each factor
$\sqrt{ 12^{2} }$ $\sqrt{ x^{6} }$ $\sqrt{ y^{4} }$ $\sqrt{xy}$
reduce the index of the radical and exponent with 2 of the first square root
12$\sqrt{ x^{6} }$ $\sqrt{ y^{4} }$ $\sqrt{xy}$
reduce the index of the radical and exponent with 2 of the second square root
12x³$\sqrt{ y^{4} }$ $\sqrt{xy}$
reduce the index of the radical and exponent with 2 of the third square root
12x³y²$\sqrt{xy}$
this means that the correct answer to your question is 12x³y²$\sqrt{xy}$ .
let me know if you have any further questions
:)