Question

How to simplify the square root of 3 over the square root of 21

Answer 1

answer: √3⋅√21 = 3√7

Answer 2

3 * 7 = 21, so

`√(21)=√(3\cdot7)=\sqrt3\sqrt7`

Then

`(\sqrt3)/(√(21))=\frac1{\sqrt7}`

and you can rationalize the denominator to write this as

`\frac1{\sqrt7}\cdot(\sqrt7)/(\sqrt7)=\frac{\sqrt7}7`