Solve 51/56*sqrt{5/98}

$$\frac { 51 } { 56 } \times \sqrt { \frac { 5 } { 98 } }$$

Evaluate

$$\frac{51\sqrt{10}}{784}\approx 0.205709389$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{5}{98}} as the division of square roots \frac{\sqrt{5}}{\sqrt{98}}.

$$\frac{51}{56}\times \frac{\sqrt{5}}{\sqrt{98}}$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$\frac{51}{56}\times \frac{\sqrt{5}}{7\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{5}}{7\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{51}{56}\times \frac{\sqrt{5}\sqrt{2}}{7\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{51}{56}\times \frac{\sqrt{5}\sqrt{2}}{7\times 2}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{51}{56}\times \frac{\sqrt{10}}{7\times 2}$$

Multiply 7 and 2 to get 14.

$$\frac{51}{56}\times \frac{\sqrt{10}}{14}$$

Multiply \frac{51}{56} times \frac{\sqrt{10}}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{51\sqrt{10}}{56\times 14}$$

Multiply 56 and 14 to get 784.

$$\frac{51\sqrt{10}}{784}$$