Question

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

Answer 1

`19sqrt(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`

`=2sqrt(4*4*3)+7sqrt(2*2*3)-sqrt(3*3*3)`

`=2*4sqrt(3)+7*2sqrt(3)-3sqrt(3)`

`=(8+14-3)sqrt(3)`

`=19sqrt(3)`