How do you simplify 2sqrt[48] + 7sqrt[12] –sqrt[27]?

May 10, 2016

$19 \sqrt{3}$

Explanation:

The key element of the simplification is to break down all the numbers into their smallest factors and identify those factors which can be taken outside the square root.

2sqrt(48)+7sqrt(12)-sqrt(27

$= 2 \sqrt{4 \cdot 4 \cdot 3} + 7 \sqrt{2 \cdot 2 \cdot 3} - \sqrt{3 \cdot 3 \cdot 3}$

$= 2 \cdot 4 \sqrt{3} + 7 \cdot 2 \sqrt{3} - 3 \sqrt{3}$

$= \left(8 + 14 - 3\right) \sqrt{3}$

$= 19 \sqrt{3}$