Solve sqrt{1frac{7/9}}{sqrt{1/9}}

$$\frac{ \sqrt{ 1 \frac{ 7 }{ 9 } } }{ \sqrt{ \frac{ 1 }{ 9 } } }$$

Evaluate

$$4$$

Solution Steps

Multiply 1 and 9 to get 9.

$$\frac{\sqrt{\frac{9+7}{9}}}{\sqrt{\frac{1}{9}}}$$

Add 9 and 7 to get 16.

$$\frac{\sqrt{\frac{16}{9}}}{\sqrt{\frac{1}{9}}}$$

Rewrite the square root of the division \frac{16}{9} as the division of square roots \frac{\sqrt{16}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{\frac{4}{3}}{\sqrt{\frac{1}{9}}}$$

Rewrite the square root of the division \frac{1}{9} as the division of square roots \frac{\sqrt{1}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{\frac{4}{3}}{\frac{1}{3}}$$

Divide \frac{4}{3} by \frac{1}{3} by multiplying \frac{4}{3} by the reciprocal of \frac{1}{3}.

$$\frac{4}{3}\times 3$$

Cancel out 3 and 3.

$$4$$

Factor

$$2^{2}$$