# How do you simplify sqrt12- sqrt 50+ sqrt 72?

Jul 16, 2017

#### Answer:

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

#### Explanation:

You are looking for squared numbers that you can 'take outside' the root and any repeated values that you can combine.

Notice that all the numbers are even so lets play with that to start with.

$\sqrt{2 \times 6} - \sqrt{2 \times 25} + \sqrt{2 \times 36}$

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

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

'Take out' the squared values

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

Note that 6 of something - 5 of something leaves 1 of something

$2 \sqrt{3} + \left[\textcolor{w h i t e}{.} 6 \sqrt{2} - 5 \sqrt{2} \textcolor{w h i t e}{.}\right]$

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

$\sqrt{12} - \sqrt{50} + \sqrt{72} \approx 4.8783 \ldots$

$2 \sqrt{3} + \sqrt{2} \approx 4.8783 \ldots .$