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

sqrt72=

Simplify. $\newline$ Remove all perfect squares from inside the square root. $\newline$ $\sqrt{72}$

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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{72}

Factor $72$ into prime factors: Factor $72$ into its prime factors. $\newline$ $72$ can be factored into $2 \times 36$ , where $36$ is a perfect square ( $6 \times 6$ ). $\newline$ So, $72 = 2 \times 2 \times 2 \times 3 \times 3$ .
Group prime factors into perfect squares: Group the prime factors into pairs of perfect squares. $\newline$ From the prime factorization, we can group the factors as follows: $(2 \times 2) \times (3 \times 3) \times 2$ .
Simplify square root by taking out perfect squares: Simplify the square root by taking out the perfect squares. $\newline$ The square root of a perfect square is the number itself, so we take the square root of each pair: $\newline$ $\sqrt{72} = \sqrt{(2 \times 2) \times (3 \times 3) \times 2} = 2 \times 3 \times \sqrt{2} = 6 \times \sqrt{2}$ .

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