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

Answer:

$18\sqrt{8}=36\sqrt{2}$

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

Step-by-step explanation:

Given problem $18\sqrt{8}$

We have to write the given problem in form of $a\sqrt{b}$, where a and b are integers and b is as small as possible.

Consider the given problem $18\sqrt{8}$

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

Substitute, in given problem, we have

$18\sqrt{8}=18\sqrt{2 \times 2\times 2}$

This can be written as,

$18\sqrt{2 \times 2\times 2}=18(\sqrt{4}\sqrt{2})$

We know $\sqrt{4}=2$ , thus,

$18(\sqrt{4}\sqrt{2})=18\cdot 2\sqrt{2}=36\sqrt{2}$

Thus,$18\sqrt{8}=36\sqrt{2}$

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

Answer 2

For this case, the first thing we are going to do is rewrite the expression.
 We have then:
 (18) / root (8)
 (18) / root (2 * 4)
 (18) / 2 * root (2)
 (9) / root (2)
 Thus, the values of a and b are:
 a = 9
 b = 2
 Answer:
 a = 9
 b = 2