Question

$\sqrt{\frac{49}{81}} = \square$

Explanation:

Step1: Recall square - root property

The square - root of a fraction $\sqrt{\frac{a}{b}}$ (where $a\geq0$ and $b > 0$) can be calculated using the property $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$. For the given expression $\sqrt{\frac{49}{81}}$, we can apply this property. So we have $\sqrt{\frac{49}{81}}=\frac{\sqrt{49}}{\sqrt{81}}$.

Step2: Calculate square - roots of numerator and denominator

We know that $7\times7 = 49$, so $\sqrt{49}=7$. Also, $9\times9 = 81$, so $\sqrt{81}=9$.

Step3: Form the fraction

Substituting the values of $\sqrt{49}$ and $\sqrt{81}$ into the fraction $\frac{\sqrt{49}}{\sqrt{81}}$, we get $\frac{7}{9}$.

Answer:

$\frac{7}{9}$