# How do you simplify 4sqrt(200)+8sqrt(49)-2sqrt2?

Apr 22, 2016

I found: $38 \sqrt{2} + 56$

#### Explanation:

I would change it by manipulating the arguments of the square roots:

$4 \sqrt{100 \cdot 2} + 8 \sqrt{{7}^{2}} - 2 \sqrt{2} =$

$= 4 \sqrt{100} \cdot \sqrt{2} + 8 \sqrt{{7}^{2}} - 2 \sqrt{2} =$

$= 4 \cdot 10 \sqrt{2} + 8 \cdot 7 - 2 \sqrt{2} =$

$= 40 \sqrt{2} + 56 - 2 \sqrt{2} =$

$= 38 \sqrt{2} + 56$

Apr 22, 2016

if $\sqrt{49} = + 7 \text{ }$ then we have: $\text{ } 38 \sqrt{2} + 56$

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Most people would go with the answer provided above.
if $\sqrt{49} = - 7 \text{ }$ then we have: $\text{ } 38 \sqrt{2} - 56$
You may also have a problem with$\text{ } \sqrt{2 \times {10}^{2}}$

#### Explanation:

Try and identify common factors such that all the roots are the same. Where you can 'get rid' of the roots.

Write as:

$\text{ } 4 \sqrt{2 \times {10}^{2}} + 8 \sqrt{{7}^{2}} - 2 \sqrt{2}$

$\text{ } 40 \sqrt{2} - 2 \sqrt{2} + 56$

$\text{ } 38 \sqrt{2} + 56$
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However, $\sqrt{49} = \pm 7$

So we could have:

$\text{ } 38 \sqrt{2} - 56$