What is the square root of 50 + square root of 18?

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What is the square root of 50 + square root of 18?

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Answer 1 · 2018-07-09T18:25:05

$8 \sqrt{2}$ $8sqrt2$

Explanation:

$50$ $50$ is the same thing as $25 \cdot 2$ $25*2$ , and $18$ $18$ is the same as $9 \cdot 2$ $9*2$ . Writing the radicals in this way allows us to factor out a perfect square.

We have:

$\sqrt{25 \cdot 2} + \sqrt{9 \cdot 2}$ $sqrt(25*2)+sqrt(9*2)$

Which simplifies to

$5 \sqrt{2} + 3 \sqrt{2}$ $5sqrt2+3sqrt2$

Since these both have $\sqrt{2}$ $sqrt2$ as a factor, we can add them to get

$8 \sqrt{2}$ $8sqrt2$

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What is the square root of 50 + square root of 18?

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