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

Sep 10, 2015

=color(blue)(4sqrt3

#### Explanation:

Simplifying $\sqrt{27}$ 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