Solve sqrt{5/8*3/8/40}

$$\sqrt { \frac { \frac { 5 } { 8 } \times \frac { 3 } { 8 } } { 40 } }$$

Evaluate

$$\frac{\sqrt{6}}{32}\approx 0.076546554$$

Solution Steps

Multiply \frac{5}{8} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{\frac{5\times 3}{8\times 8}}{40}}$$

Do the multiplications in the fraction \frac{5\times 3}{8\times 8}.

$$\sqrt{\frac{\frac{15}{64}}{40}}$$

Express \frac{\frac{15}{64}}{40} as a single fraction.

$$\sqrt{\frac{15}{64\times 40}}$$

Multiply 64 and 40 to get 2560.

$$\sqrt{\frac{15}{2560}}$$

Reduce the fraction \frac{15}{2560} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{3}{512}}$$

Rewrite the square root of the division \sqrt{\frac{3}{512}} as the division of square roots \frac{\sqrt{3}}{\sqrt{512}}.

$$\frac{\sqrt{3}}{\sqrt{512}}$$

Factor 512=16^{2}\times 2. Rewrite the square root of the product \sqrt{16^{2}\times 2} as the product of square roots \sqrt{16^{2}}\sqrt{2}. Take the square root of 16^{2}.

$$\frac{\sqrt{3}}{16\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{3}}{16\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{3}\sqrt{2}}{16\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{3}\sqrt{2}}{16\times 2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{16\times 2}$$

Multiply 16 and 2 to get 32.

$$\frac{\sqrt{6}}{32}$$