Solve 4sqrt{214/25}+sqrt{36/64}=

$$4 \sqrt { 2 \frac { 14 } { 25 } } + \sqrt { \frac { 36 } { 64 } } =$$

Evaluate

$$\frac{143}{20}=7.15$$

Solution Steps

Multiply 2 and 25 to get 50.

$$4\sqrt{\frac{50+14}{25}}+\sqrt{\frac{36}{64}}$$

Add 50 and 14 to get 64.

$$4\sqrt{\frac{64}{25}}+\sqrt{\frac{36}{64}}$$

Rewrite the square root of the division \frac{64}{25} as the division of square roots \frac{\sqrt{64}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$4\times \frac{8}{5}+\sqrt{\frac{36}{64}}$$

Express 4\times \frac{8}{5} as a single fraction.

$$\frac{4\times 8}{5}+\sqrt{\frac{36}{64}}$$

Multiply 4 and 8 to get 32.

$$\frac{32}{5}+\sqrt{\frac{36}{64}}$$

Reduce the fraction \frac{36}{64} to lowest terms by extracting and canceling out 4.

$$\frac{32}{5}+\sqrt{\frac{9}{16}}$$

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

$$\frac{32}{5}+\frac{3}{4}$$

Least common multiple of 5 and 4 is 20. Convert \frac{32}{5} and \frac{3}{4} to fractions with denominator 20.

$$\frac{128}{20}+\frac{15}{20}$$

Since \frac{128}{20} and \frac{15}{20} have the same denominator, add them by adding their numerators.

$$\frac{128+15}{20}$$

Add 128 and 15 to get 143.

$$\frac{143}{20}$$

Factor

$$\frac{11 \cdot 13}{2 ^ {2} \cdot 5} = 7\frac{3}{20} = 7.15$$