Question

evaluate: $\left(\frac{25}{36}\
ight)^{\frac{1}{2}}$ \
\
\\(\bigcirc\\) a. $\frac{25}{36}$ \
\\(\bigcirc\\) b. $\frac{5}{6}$ \
\\(\bigcirc\\) c. $\frac{5}{36}$ \
\\(\bigcirc\\) d. $\frac{25}{6}$

Explanation:

Step1: Recall the exponent rule for square roots

The formula for \((\frac{a}{b})^{\frac{1}{2}}\) is \(\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\) (where \(a\geq0\), \(b > 0\)). For \((\frac{25}{36})^{\frac{1}{2}}\), we can apply this rule.

Step2: Calculate the square roots of numerator and denominator

We know that \(\sqrt{25} = 5\) because \(5\times5=25\), and \(\sqrt{36}=6\) because \(6\times6 = 36\). So \(\frac{\sqrt{25}}{\sqrt{36}}=\frac{5}{6}\).

Answer:

B. \(\frac{5}{6}\)