Question

which of the following is equal to square root 18x^7y^6?

Answer 1

square root 18x^7y^6
=(18x^7y^6)^1/2
(9*2*x^6*X*y^6)^1/2
=   3 x3y3 • sqrt(2x) 
hope this helps

Answer 2

Answer:

To find the square root of $18x^7y^6$  i.e,  $\sqrt{18x^7y^6}$

Using radical rules:

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

$(a^m)^{\frac{1}{n}} = a^{\frac{m}{n}}$

we can write:

$18 = 3 \cdot 3 \cdot 2 = 3^2 \cdot 2$

$x^7 = x^6 \cdot x$

then;

$\sqrt{18x^7y^6}$ = $\sqrt{3^2 \cdot 2 \cdot x^6 \cdot x \cdot y^6}$

Apply the rules we have;

$3 \cdot x^3 \cdot y^3 \cdot \sqrt{2x}$

or

$3x^3y^3\sqrt{2x}$

therefore, $3x^3y^3\sqrt{2x}$ is equal to $\sqrt{18x^7y^6}$