Question

Change the radical √5/√8

into simplest radical form a/b √c, where a, b, and c are all integers.

Answer 1

`(√(5))/(√(8))=(1)/(4)\sqrt{10`

Explanation:

Given

`(√(5))/(√(8))`

Required

Express in its simplest form

To do this, we simply radicalize the given expression by multiplying the expression by the denominator over the denominator.

In other words:

`(√(5))/(√(8)) * (√(8))/(√(8))`

`(√(5)*√(8))/(√(8)*√(8))`

`(√(40))/(√(64))`

Take positive square root

`(√(40))/(8)`

Express 40 as 4 * 10

`(√(4*10))/(8)`

`(√(4)*√(10))/(8)`

`(2*√(10))/(8)`

Simplify:

`(1*√(10))/(4)`

`=(1)/(4)\sqrt{10`

Hence:

`(√(5))/(√(8))=(1)/(4)\sqrt{10`