# How do you simplify 3sqrt27+4sqrt12-sqrt300?

Oct 4, 2017

$7 \sqrt{3}$

#### Explanation:

$3 \sqrt{27} + 4 \sqrt{12} - \sqrt{300}$

$= 3 \sqrt{9 \times 3} + 4 \sqrt{4 \times 3} - \sqrt{100 \times 3}$
$= 3 \sqrt{9} \sqrt{3} + 4 \sqrt{4} \sqrt{3} - \sqrt{100} \sqrt{3}$
$= \left(3 \times 3\right) \sqrt{3} + \left(4 \times 2\right) \sqrt{3} - 10 \sqrt{3}$
$= 9 \sqrt{3} + 8 \sqrt{3} - 10 \sqrt{3}$
$= 17 \sqrt{3} - 10 \sqrt{3}$
$= 7 \sqrt{3}$

Oct 4, 2017

$3 \sqrt{27} + 4 \sqrt{12} - \sqrt{300} = 7 \sqrt{3}$

#### Explanation:

To answer this question, you need to get each number to the same root. You cannot do anything with them now, but by giving them a square root in common you can simplify this expression.

This is best worked out by splitting each part of the expression up:

$3 \sqrt{27} = 3 \sqrt{9 \cdot 3} = 3 \cdot \sqrt{9} \cdot \sqrt{3} = 3 \cdot 3 \cdot \sqrt{3} = 9 \sqrt{3}$

In short, $3 \sqrt{27} = 9 \sqrt{3}$

Similarly,

$4 \sqrt{12} = 4 \sqrt{4 \cdot 3} = 4 \cdot \sqrt{4} \cdot \sqrt{3} = 4 \cdot 2 \cdot \sqrt{3} = 8 \sqrt{3}$

In short, $4 \sqrt{12} = 8 \sqrt{3}$

And then again:

$\sqrt{300} = \sqrt{100 \cdot 3} = \sqrt{100} \cdot \sqrt{3} = 10 \cdot \sqrt{3} = 10 \sqrt{3}$

In short, $\sqrt{300} = 10 \sqrt{3}$

Putting these together we get:
$9 \sqrt{3} + 8 \sqrt{3} - 10 \sqrt{3}$
$= 7 \sqrt{3}$