Question

What is the square root of 5 divided by the square root of 15 and simplify and in fraction form​

Answer 1

`\sqrt{(1)/(3) }`

or

`(√(3) )/(3)`

Explanation:

The expression
`(√(5) )/(√(15) )` can be simplified by first writing the fraction under one single radical instead of two.

`(√(5) )/(√(15) ) = \sqrt{(5)/(15) }`

5/15 simplifies because both share the same factor 5.

It becomes
`\sqrt{(5)/(15) } = \sqrt{(1)/(3) }`

This can simplify further by breaking apart the radical.

`\sqrt{(1)/(3) }  = (√(1) )/(√(3) )  = (1)/(√(3) )`

A radical cannot be left in the denominator, so rationalize it by multiplying by √3 to numerator and denominator.

`(1)/(√(3) ) *(√(3) )/(√(3) )  =(√(3) )/(3)`