# How do you simplify sqrt[12] - sqrt[147]?

Jun 22, 2016

$\implies - 5 \sqrt{3}$

#### Explanation:

Looking for common factors

If you are not sure what numbers to use build factor trees. Split the numbers up into prime numbers and looked for squared numbers that can be 'extracted' from the square roots.

Note that the sum of the digits for 12 is 3 and the sum of the digits for 147 is 12. Both of these sums are divisible by 3 so the original numbers are divisible by 3 as well,

$147 = 3 \times {7}^{2}$
$12 = 3 \times {2}^{2}$

$\sqrt{12} - \sqrt{147} \text{ "=" } \sqrt{3 \times {2}^{2}} - \sqrt{3 \times {7}^{2}}$

$\implies 2 \sqrt{3} - 7 \sqrt{3}$

$\textcolor{b r o w n}{\text{we are now counting how many of "sqrt(3)" we have got giving:}}$

$\implies - 5 \sqrt{3}$