How do you solve $\sqrt{50} + \sqrt{2}$ $sqrt(50)+sqrt(2)$ ?

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How do you solve $\sqrt{50} + \sqrt{2}$ $sqrt(50)+sqrt(2)$ ?

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Answer 1 · 2015-09-09T22:01:45

You can simplify $\sqrt{50} + \sqrt{2} = 6 \sqrt{2}$ $sqrt(50)+sqrt(2) = 6sqrt(2)$

Explanation:

If $a, b \geq 0$ $a, b >= 0$ then $\sqrt{a b} = \sqrt{a} \sqrt{b}$ $sqrt(ab) = sqrt(a)sqrt(b)$ and $\sqrt{a^{2}} = a$ $sqrt(a^2) = a$

So:

$\sqrt{50} + \sqrt{2} = \sqrt{5^{2} \cdot 2} + \sqrt{2} = \sqrt{5^{2}} \sqrt{2} + \sqrt{2}$ $sqrt(50)+sqrt(2) = sqrt(5^2*2)+sqrt(2) = sqrt(5^2)sqrt(2) + sqrt(2)$

$= 5 \sqrt{2} + 1 \sqrt{2} = (5 + 1) \sqrt{2} = 6 \sqrt{2}$ $= 5sqrt(2)+1sqrt(2) = (5+1)sqrt(2) = 6sqrt(2)$

In general you can try to simplify $\sqrt{n}$ $sqrt(n)$ by factorising $n$ $n$ to identify square factors. Then you can move the square roots of those square factors out from under the square root.

e.g. $\sqrt{300} = \sqrt{10^{2} \cdot 3} = 10 \sqrt{3}$ $sqrt(300) = sqrt(10^2*3) = 10sqrt(3)$

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How do you solve $\sqrt{50} + \sqrt{2}$ $sqrt(50)+sqrt(2)$ ?

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How do you solve $\sqrt{50} + \sqrt{2}$ $sqrt(50)+sqrt(2)$ ?