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

sqrt180=

Simplify. $\newline$ Remove all perfect squares from inside the square root. $\newline$ $\sqrt{180}$

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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{180}

Factorize the number $180$ : Factorize the number $180$ to find perfect squares. $\newline$ We need to find the prime factorization of $180$ to identify any perfect squares that can be taken out of the square root. $\newline$ $180 = 2 \times 90$ $\newline$ $180 = 2 \times 2 \times 45$ $\newline$ $180 = 2 \times 2 \times 5 \times 9$ $\newline$ $180 = 2^2 \times 5 \times 3^2$
Identify and take out perfect squares: Identify and take out the perfect squares from the square root. $\newline$ We have identified $2^2$ and $3^2$ as perfect squares. We can take the square root of these perfect squares and move them outside the square root. $\newline$ $\sqrt{180} = \sqrt{2^2 \times 5 \times 3^2}$ $\newline$ $\sqrt{180} = \sqrt{2^2} \times \sqrt{3^2} \times \sqrt{5}$ $\newline$ $\sqrt{180} = 2 \times 3 \times \sqrt{5}$
Simplify the expression: Simplify the expression. $\newline$ After taking out the perfect squares, we are left with the square root of $5$ , which cannot be simplified further. $\newline$ Therefore, the simplified form of $\sqrt{180}$ is: $\newline$ $2 \times 3 \times \sqrt{5}$ $\newline$ Which simplifies to: $\newline$ $6 \times \sqrt{5}$

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