How do you simplify 3sqrt[3] + 2sqrt[27] –sqrt[12]?

Apr 8, 2016

$7 \sqrt{3}$

Explanation:

Given an expression to simply
$3 \sqrt{3} + 2 \sqrt{27} - \sqrt{12}$
Factorize second and third terms as

3sqrt3+2sqrt(3xx3xx3)-sqrt(2xx2xx3

We know that if there are 2 same digits/numbers under the square root symbol, these can be taken outside the symbol with the condition that the digit/number is written only once outside the symbol. Following this we obtain

$3 \sqrt{3} + 2 \times 3 \sqrt{3} - 2 \sqrt{3}$,
simplifying and taking out common factor $\sqrt{3}$ gives us
or $3 \sqrt{3} + 6 \sqrt{3} - 2 \sqrt{3}$
or $\sqrt{3} \left(3 + 6 - 2\right)$,
simplifying numbers inside the parenthesis we obtain
$7 \sqrt{3}$