Answer:
C. [tex]\sqrt{\frac{25}{36} }[/tex]
Step-by-step explanation:
This comes from the property of exponents which says for any numbers [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex],
[tex](a*b)^c=a^c*b^c[/tex]
Since square roots are just exponents of [tex]\frac{1}{2}[/tex] power ([tex]\sqrt{x} =x^\frac{1}{2}[/tex]), and [tex]\frac{1}{x} =x^{-1}[/tex], we have
[tex]\frac{\sqrt{25}}{\sqrt{36} }=25^{\frac{1}{2} }*36^{-\frac{1}{2} }=25^{\frac{1}{2} }*(36^{-1})^{\frac{1}{2} }=(25*(36^{-1})})^{\frac{1}{2}[/tex]
[tex]=\sqrt{25*36^{-1}} =\sqrt{\frac{25}{36} }[/tex]
Which is choice C.
