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.
Accepted Solution
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Answer:[tex]18\sqrt{8}=36\sqrt{2}[/tex]Where a=36 and b=2 with b is small.Step-by-step explanation:Given problem [tex]18\sqrt{8}[/tex]We have to write the given problem in form of [tex]a\sqrt{b}[/tex], where a and b are integers and b is as small as possible.Consider the given problem [tex]18\sqrt{8}[/tex]8 can be written in factored form as 2 × 2 × 2Substitute, in given problem, we have [tex]18\sqrt{8}=18\sqrt{2 \times 2\times 2}[/tex]This can be written as, [tex]18\sqrt{2 \times 2\times 2}=18(\sqrt{4}\sqrt{2})[/tex]We know [tex]\sqrt{4}=2[/tex] , thus, [tex]18(\sqrt{4}\sqrt{2})=18\cdot 2\sqrt{2}=36\sqrt{2}[/tex]Thus,[tex]18\sqrt{8}=36\sqrt{2}[/tex]Where a=36 and b=2 with b is small.