Question

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

Answer 1

`7sqrt3`

Explanation:

Given an expression to simply
`3sqrt3+2sqrt27-sqrt12`
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

`3sqrt3+2xx3sqrt3-2sqrt3`,
simplifying and taking out common factor `sqrt3` gives us
or `3sqrt3+6sqrt3-2sqrt3`
or `sqrt3(3+6-2)`,
simplifying numbers inside the parenthesis we obtain
`7sqrt3`