Solve sqrt{64/49+32/7}

$$\sqrt { \frac { 64 } { 49 } + \frac { 32 } { 7 } }$$

Evaluate

$$\frac{12\sqrt{2}}{7}\approx 2.424366107$$

Solution Steps

Least common multiple of 49 and 7 is 49. Convert \frac{64}{49} and \frac{32}{7} to fractions with denominator 49.

$$\sqrt{\frac{64}{49}+\frac{224}{49}}$$

Since \frac{64}{49} and \frac{224}{49} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{64+224}{49}}$$

Add 64 and 224 to get 288.

$$\sqrt{\frac{288}{49}}$$

Rewrite the square root of the division \sqrt{\frac{288}{49}} as the division of square roots \frac{\sqrt{288}}{\sqrt{49}}.

$$\frac{\sqrt{288}}{\sqrt{49}}$$

Factor 288=12^{2}\times 2. Rewrite the square root of the product \sqrt{12^{2}\times 2} as the product of square roots \sqrt{12^{2}}\sqrt{2}. Take the square root of 12^{2}.

$$\frac{12\sqrt{2}}{\sqrt{49}}$$

Calculate the square root of 49 and get 7.

$$\frac{12\sqrt{2}}{7}$$