Solve sqrt{61/4}*sqrt{17/9}

$$\sqrt { 6 \frac { 1 } { 4 } } \times \sqrt { 1 \frac { 7 } { 9 } }$$

Evaluate

$$\frac{10}{3}\approx 3.333333333$$

Solution Steps

Multiply 6 and 4 to get 24.

$$\sqrt{\frac{24+1}{4}}\sqrt{\frac{1\times 9+7}{9}}$$

Add 24 and 1 to get 25.

$$\sqrt{\frac{25}{4}}\sqrt{\frac{1\times 9+7}{9}}$$

Rewrite the square root of the division \frac{25}{4} as the division of square roots \frac{\sqrt{25}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{5}{2}\sqrt{\frac{1\times 9+7}{9}}$$

Multiply 1 and 9 to get 9.

$$\frac{5}{2}\sqrt{\frac{9+7}{9}}$$

Add 9 and 7 to get 16.

$$\frac{5}{2}\sqrt{\frac{16}{9}}$$

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.

$$\frac{5}{2}\times \frac{4}{3}$$

Multiply \frac{5}{2} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 4}{2\times 3}$$

Do the multiplications in the fraction \frac{5\times 4}{2\times 3}.

$$\frac{20}{6}$$

Reduce the fraction \frac{20}{6} to lowest terms by extracting and canceling out 2.

$$\frac{10}{3}$$

Factor

$$\frac{2 \cdot 5}{3} = 3\frac{1}{3} = 3.3333333333333335$$