# How do you simplify sqrt3*sqrt27?

Jun 13, 2016

$= 9$

#### Explanation:

$\sqrt{3} \cdot \sqrt{27}$

$\sqrt{27}$ can be simplified by prime factorisation. (expressing a number as a product of its prime factors)

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

The expression can now be written as:
sqrt3 * sqrt27 = sqrt 3 * color(blue)(3sqrt3

= 3 * sqrt 3 * color(blue)(sqrt3

$= 3 \cdot 3$

$= 9$

Jun 14, 2016

= $\sqrt{81} = 9$

#### Explanation:

When multiplying or dividing with roots, two roots can be combined into one root.

$\sqrt{3} \times \sqrt{27} = \sqrt{3 \times 27}$

= $\sqrt{81}$

$= 9$