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Square root addition or sub
Simplify.

-sqrt75+5sqrt12

Square root addition or sub $\newline$ Simplify. $\newline$ $-\sqrt{75}+5 \sqrt{12}$

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Simplify radical expressions: mixed review

Full solution

Q. Square root addition or sub

\newline

Simplify.

\newline

-\sqrt{75}+5 \sqrt{12}

Simplify $-\sqrt{75}$ : Simplify $-\sqrt{75}$ . $\newline$ Prime factorization of $75$ is $3 \times 5^2$ . $\newline$ So, $-\sqrt{75}$ = $-\sqrt{3 \times 5^2}$ .
Take out square factor: Now, take out the square factor from under the square root. $\newline$ $-\sqrt{3 \times 5^2} = -5\sqrt{3}$ .
Simplify $5\sqrt{12}$ : Next, simplify $5\sqrt{12}$ . Prime factorization of $12$ is $2 \times 2 \times 3$ . So, $5\sqrt{12}$ = $5\sqrt{2^2 \times 3}$ .
Take out square factor: Take out the square factor from under the square root. $5\sqrt{2^2 \times 3} = 5 \times 2\sqrt{3}.$
Combine like terms: Now, we have $-5\sqrt{3} + 10\sqrt{3}$ . $\newline$ Combine the like terms. $\newline$ $-5\sqrt{3} + 10\sqrt{3} = 5\sqrt{3}$ .

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