Solve sqrt{61/4}*sqrt{111/25}

$$\sqrt { 6 \frac { 1 } { 4 } } \cdot \sqrt { 1 \frac { 11 } { 25 } }$$

Evaluate

$$3$$

Solution Steps

Multiply 6 and 4 to get 24.

$$\sqrt{\frac{24+1}{4}}\sqrt{\frac{1\times 25+11}{25}}$$

Add 24 and 1 to get 25.

$$\sqrt{\frac{25}{4}}\sqrt{\frac{1\times 25+11}{25}}$$

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.

$$\frac{5}{2}\sqrt{\frac{1\times 25+11}{25}}$$

Multiply 1 and 25 to get 25.

$$\frac{5}{2}\sqrt{\frac{25+11}{25}}$$

Add 25 and 11 to get 36.

$$\frac{5}{2}\sqrt{\frac{36}{25}}$$

Rewrite the square root of the division \frac{36}{25} as the division of square roots \frac{\sqrt{36}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{5}{2}\times \frac{6}{5}$$

Multiply \frac{5}{2} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 6}{2\times 5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{6}{2}$$

Divide 6 by 2 to get 3.

$$3$$

Factor

$$3$$