Question

What is the square root of 3 plus the square root of 27?

Answer 1

`=color(blue)(4sqrt3`

Explanation:

Simplifying `sqrt27` by prime factorisation:

`sqrt27 = sqrt(3*3*3) = sqrt(3^2*3) = color(blue)(3sqrt3`

The expression can now be expressed as
`sqrt3 +sqrt27 = sqrt3 +color(blue)(3sqrt3`

`=color(blue)(4sqrt3`