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

sqrt450=

Simplify. $\newline$ Remove all perfect squares from inside the square root. $\newline$ $\sqrt{450}$

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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{450}

Factor $450$ into prime factors: Factor $450$ into its prime factors. $\newline$ $450$ can be factored into $2 \times 225$ , and $225$ is a perfect square ( $15 \times 15$ ). So, we can write $450$ as $2 \times 15^2$ .
Apply square root to factors: Apply the square root to the factors. $\newline$ The square root of a product is the product of the square roots, so $\sqrt{450} = \sqrt{2 \times 15^2}$ .
Simplify square root of perfect square: Simplify the square root of the perfect square. $\newline$ Since $15^2$ is a perfect square, its square root is $15$ . Therefore, $\sqrt{450} = \sqrt{2} \times \sqrt{15^2} = \sqrt{2} \times 15$ .
Write final simplified form: Write the final simplified form. $\newline$ The simplified form of $\sqrt{450}$ is $15 \times \sqrt{2}$ .

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