Question $\newline$ Watch Video $\newline$ Show Examples $\newline$ Assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $\newline$ $\sqrt{180 x^{7} y^{3}}$ $\newline$ Answer Attempt $2$ out of $2$

Full solution

Q. Question

\newline

Watch Video

\newline

Show Examples

\newline

Assuming

x

and

y

are both positive, write the following expression in simplest radical form.

\newline

\sqrt{180 x^{7} y^{3}}

\newline

Answer Attempt

2

out of

2

Question Prompt: Question prompt: Simplify $\sqrt{180x^{7}y^{3}}$ assuming $x$ and $y$ are positive.
Factor Prime Numbers: Factor $180$ into prime factors: $180 = 2 \times 2 \times 3 \times 3 \times 5$ .
Write Perfect Squares: Write $x^{7}$ as $x^{6} \times x$ and $y^{3}$ as $y^{2} \times y$ to make perfect squares: $x^{7} = x^{6} \times x$ , $y^{3} = y^{2} \times y$ .
Combine Factors: Combine the factors under the square root: $\sqrt{180x^{7}y^{3}} = \sqrt{2 \times 2 \times 3 \times 3 \times 5 \times x^{6} \times x \times y^{2} \times y}$ .
Take Out Perfect Squares: Take out the perfect squares from under the square root: $\sqrt{2^2 \times 3^2 \times 5 \times x^{6} \times x \times y^{2} \times y} = 2 \times 3 \times x^{3} \times y \times \sqrt{5xy}$ .
Simplify Expression: Simplify the expression: $2 \times 3 \times x^{3} \times y \times \sqrt{5xy} = 6x^{3}y \sqrt{5xy}.$