Answer:
[tex]\frac{\sqrt{5}}{\sqrt{8}}=\frac{1}{4}\sqrt{10[/tex]
Step-by-step explanation:
Given
[tex]\frac{\sqrt{5}}{\sqrt{8}}[/tex]
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:
[tex]\frac{\sqrt{5}}{\sqrt{8}} * \frac{\sqrt{8}}{\sqrt{8}}[/tex]
[tex]\frac{\sqrt{5}*\sqrt{8}}{\sqrt{8}*\sqrt{8}}[/tex]
[tex]\frac{\sqrt{40}}{\sqrt{64}}[/tex]
Take positive square root
[tex]\frac{\sqrt{40}}{8}[/tex]
Express 40 as 4 * 10
[tex]\frac{\sqrt{4*10}}{8}[/tex]
[tex]\frac{\sqrt{4}*\sqrt{10}}{8}[/tex]
[tex]\frac{2*\sqrt{10}}{8}[/tex]
Simplify:
[tex]\frac{1*\sqrt{10}}{4}[/tex]
[tex]=\frac{1}{4}\sqrt{10[/tex]
Hence:
[tex]\frac{\sqrt{5}}{\sqrt{8}}=\frac{1}{4}\sqrt{10[/tex]
