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Simplify.
Remove all perfect squares from inside the square root.

sqrt175=

Simplify. $\newline$ Remove all perfect squares from inside the square root. $\newline$ $\sqrt{175}=$

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Simplify radical expressions with variables

Full solution

Q. Simplify.

\newline

Remove all perfect squares from inside the square root.

\newline

\sqrt{175}=

Factorizing $175$ : First, we need to factor $175$ into its prime factors to identify any perfect squares. $\newline$ $175 = 5 \times 35$ $\newline$ $175 = 5 \times 5 \times 7$ $\newline$ Now we have found that $5^2$ is a perfect square within the factorization of $175$ .
Rewriting the square root: Next, we can rewrite the square root of $175$ as the square root of the product of its prime factors, separating the perfect square. $\newline$ $\sqrt{175} = \sqrt{5^2 \times 7}$
Taking out the perfect square: Now, we can take the square root of the perfect square $5^2$ out of the radical. $\sqrt{5^2 \times 7} = 5 \times \sqrt{7}$
Simplifying the expression: We have now removed all perfect squares from inside the square root, and the expression is simplified. $\newline$ The final answer is $5 \times \sqrt{7}$ .

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