Solve sqrt{6(11/5)^2-2(11/3)^2}=

$$\sqrt { 6 ( \frac { 11 } { 5 } ) ^ { 2 } - 2 ( \frac { 11 } { 3 } ) ^ { 2 } } =$$

Evaluate

$$\frac{22}{15}\approx 1.466666667$$

Solution Steps

Calculate \frac{11}{5} to the power of 2 and get \frac{121}{25}.

$$\sqrt{6\times \frac{121}{25}-2\times \left(\frac{11}{3}\right)^{2}}$$

Express 6\times \frac{121}{25} as a single fraction.

$$\sqrt{\frac{6\times 121}{25}-2\times \left(\frac{11}{3}\right)^{2}}$$

Multiply 6 and 121 to get 726.

$$\sqrt{\frac{726}{25}-2\times \left(\frac{11}{3}\right)^{2}}$$

Calculate \frac{11}{3} to the power of 2 and get \frac{121}{9}.

$$\sqrt{\frac{726}{25}-2\times \frac{121}{9}}$$

Express 2\times \frac{121}{9} as a single fraction.

$$\sqrt{\frac{726}{25}-\frac{2\times 121}{9}}$$

Multiply 2 and 121 to get 242.

$$\sqrt{\frac{726}{25}-\frac{242}{9}}$$

Least common multiple of 25 and 9 is 225. Convert \frac{726}{25} and \frac{242}{9} to fractions with denominator 225.

$$\sqrt{\frac{6534}{225}-\frac{6050}{225}}$$

Since \frac{6534}{225} and \frac{6050}{225} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{6534-6050}{225}}$$

Subtract 6050 from 6534 to get 484.

$$\sqrt{\frac{484}{225}}$$

Rewrite the square root of the division \frac{484}{225} as the division of square roots \frac{\sqrt{484}}{\sqrt{225}}. Take the square root of both numerator and denominator.

$$\frac{22}{15}$$

Factor

$$\frac{2 \cdot 11}{3 \cdot 5} = 1\frac{7}{15} = 1.4666666666666666$$