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Simplify.
Remove all perfect squares from inside the square root. Assume
y is positive.

sqrt(39y^(9))=

Simplify. $\newline$ Remove all perfect squares from inside the square root. Assume $\newline$ $y$ is positive. $\newline$ $\sqrt{39y^{9}}=$

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Simplify radical expressions with variables

Full solution

Q. Simplify.

\newline

Remove all perfect squares from inside the square root. Assume

\newline

y

is positive.

\newline

\sqrt{39y^{9}}=

Identify Factorization: Identify the complete factorization of $39y^9$ . $\newline$ The prime factorization of $39$ is $3 \times 13$ . Since $y^9$ is $y$ raised to an odd power, we can factor out $y^8$ as $(y^4)^2$ , which is a perfect square, and we are left with a single $y$ . $\newline$ Complete factorization of $39y^9 = 3 \times 13 \times (y^4)^2 \times y$
Rewrite using Factorization: Rewrite the square root of the expression using the factorization. $\newline$ We have $\sqrt{39y^9} = \sqrt{3 \times 13 \times (y^4)^2 \times y}$
Simplify Square Root: Simplify the square root by taking out the perfect square. $\newline$ We can take the square root of $(y^4)^2$ , which is $y^4$ , out of the square root. $\newline$ So, $\sqrt{39y^9}$ becomes $y^4 \cdot \sqrt{3 \cdot 13 \cdot y}$ = $y^4 \cdot \sqrt{39y}$

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