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

sqrt200=

Simplify. $\newline$ Remove all perfect squares from inside the square root. $\newline$ $\sqrt{200}=$

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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{200}=

Factorize the number $200$ : Factorize the number $200$ to find perfect squares. $\newline$ The prime factorization of $200$ is $2 \times 2 \times 2 \times 5 \times 5$ , which can also be written as $2^3 \times 5^2$ .
Identify and separate perfect squares: Identify and separate the perfect squares from the prime factorization. $\newline$ We have a perfect square of $5^2$ and we can pair two of the $2$ 's to form another perfect square, $2^2$ . The remaining factor is $2$ .
Rewrite the square root of $200$ : Rewrite the square root of $200$ using the identified perfect squares. $\sqrt{200} = \sqrt{2^2 \times 5^2 \times 2}$
Simplify the square root: Simplify the square root by taking the square root of the perfect squares. $\sqrt{2^2 \cdot 5^2 \cdot 2} = \sqrt{2^2} \cdot \sqrt{5^2} \cdot \sqrt{2}$
Calculate the square roots: Calculate the square roots of the perfect squares and simplify the expression. $\sqrt{2^2} \times \sqrt{5^2} \times \sqrt{2} = 2 \times 5 \times \sqrt{2}$
Multiply the numbers outside the square root: Multiply the numbers outside the square root and write the final simplified form. $\newline$ $2 \times 5 \times \sqrt{2} = 10 \times \sqrt{2}$

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