Question

This is the first part of a three-part problem. express $18\sqrt 8$ in the form $a\sqrt b$, where $a$ and $b$ are integers and $b$ is as small as possible.

Answer 1

`18√(8)=36√(2)`

Where a=36 and b=2 with b is small.

Explanation:

Given problem
`18√(8)`

We have to write the given problem in form of
`a√(b)`, where a and b are integers and b is as small as possible.

Consider the given problem
`18√(8)`

8 can be written in factored form as 2 × 2 × 2

Substitute, in given problem, we have

`18√(8)=18√(2 * 2* 2)`

This can be written as,

`18√(2 * 2* 2)=18(√(4)√(2))`

We know
`√(4)=2` , thus,

`18(√(4)√(2))=18\cdot 2√(2)=36√(2)`

Thus,
`18√(8)=36√(2)`

Where a=36 and b=2 with b is small.