Answer:
[tex]\frac{7\sqrt{5} }{8}[/tex]
Step-by-step explanation:
Using the rules of radicals
[tex]\sqrt{\frac{a}{b} }[/tex] = [tex]\frac{\sqrt{a} }{\sqrt{b} }[/tex]
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Given
[tex]\sqrt{\frac{245}{64} }[/tex] = [tex]\frac{\sqrt{245} }{\sqrt{64} }[/tex]
Simplifying the radicals
[tex]\sqrt{245}[/tex]
= [tex]\sqrt{5(7)(7)}[/tex]
= [tex]\sqrt{49(5)}[/tex]
= [tex]\sqrt{49}[/tex] × [tex]\sqrt{5}[/tex] = 7[tex]\sqrt{5}[/tex]
and
[tex]\sqrt{64}[/tex] = 8
The simplified radical is
[tex]\frac{7\sqrt{5} }{8}[/tex]
