# How do you simplify 2 squareroot of 27 minus square root of 75 plus square root of 24?

Feb 18, 2016

$\sqrt{3} \textcolor{w h i t e}{.} \left(1 + 2 \sqrt{2}\right)$

#### Explanation:

color(blue)("Given: "2 xxsqrt(27)-sqrt(75)+sqrt(24)

Note that simplify is not 'solve'
Looking for a common factor I have spotted $\sqrt{3}$

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Consider:
$\sqrt{27} \text{ "=" " sqrt(3xx3xx3)" "=" "sqrt(3xx3^2)" " =" } 3 \sqrt{3}$

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Consider:
$\sqrt{75} \text{ "=" "sqrt(5xx15)" "=" "sqrt(3xx5^2)" "=" } 5 \sqrt{3}$

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Consider:
$\sqrt{24} \text{ "=" "sqrt(3xx8) " "=" "sqrt(3xx2xx2^2)" "=" } 2 \sqrt{3} \sqrt{2}$

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$\textcolor{b l u e}{\text{Putting this all together:}}$

$6 \sqrt{3} - 5 \sqrt{3} + 2 \sqrt{3} \sqrt{2}$

$\sqrt{3} + 2 \sqrt{3} \sqrt{2}$

$\sqrt{3} \left(1 + 2 \sqrt{2}\right)$