Solve 96+sqrt{332/63}

$$96+ \sqrt{ \frac{ 332 }{ 63 } }$$

Evaluate

$$\frac{2\sqrt{581}}{21}+96\approx 98.295613484$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{332}{63}} as the division of square roots \frac{\sqrt{332}}{\sqrt{63}}.

$$96+\frac{\sqrt{332}}{\sqrt{63}}$$

Factor 332=2^{2}\times 83. Rewrite the square root of the product \sqrt{2^{2}\times 83} as the product of square roots \sqrt{2^{2}}\sqrt{83}. Take the square root of 2^{2}.

$$96+\frac{2\sqrt{83}}{\sqrt{63}}$$

Factor 63=3^{2}\times 7. Rewrite the square root of the product \sqrt{3^{2}\times 7} as the product of square roots \sqrt{3^{2}}\sqrt{7}. Take the square root of 3^{2}.

$$96+\frac{2\sqrt{83}}{3\sqrt{7}}$$

Rationalize the denominator of \frac{2\sqrt{83}}{3\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$96+\frac{2\sqrt{83}\sqrt{7}}{3\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$96+\frac{2\sqrt{83}\sqrt{7}}{3\times 7}$$

To multiply \sqrt{83} and \sqrt{7}, multiply the numbers under the square root.

$$96+\frac{2\sqrt{581}}{3\times 7}$$

Multiply 3 and 7 to get 21.

$$96+\frac{2\sqrt{581}}{21}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 96 times \frac{21}{21}.

$$\frac{96\times 21}{21}+\frac{2\sqrt{581}}{21}$$

Since \frac{96\times 21}{21} and \frac{2\sqrt{581}}{21} have the same denominator, add them by adding their numerators.

$$\frac{96\times 21+2\sqrt{581}}{21}$$

Do the multiplications in 96\times 21+2\sqrt{581}.

$$\frac{2016+2\sqrt{581}}{21}$$