Solve sqrt{8/7*(0.15-0.140625)}

$$\sqrt{ \frac{ 8 }{ 7 } \times (0.15-0.140625) }$$

Evaluate

$$\frac{\sqrt{210}}{140}\approx 0.103509834$$

Solution Steps

Subtract 0.140625 from 0.15 to get 0.009375.

$$\sqrt{\frac{8}{7}\times 0.009375}$$

Convert decimal number 0.009375 to fraction \frac{9375}{1000000}. Reduce the fraction \frac{9375}{1000000} to lowest terms by extracting and canceling out 3125.

$$\sqrt{\frac{8}{7}\times \frac{3}{320}}$$

Multiply \frac{8}{7} times \frac{3}{320} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{8\times 3}{7\times 320}}$$

Do the multiplications in the fraction \frac{8\times 3}{7\times 320}.

$$\sqrt{\frac{24}{2240}}$$

Reduce the fraction \frac{24}{2240} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{3}{280}}$$

Rewrite the square root of the division \sqrt{\frac{3}{280}} as the division of square roots \frac{\sqrt{3}}{\sqrt{280}}.

$$\frac{\sqrt{3}}{\sqrt{280}}$$

Factor 280=2^{2}\times 70. Rewrite the square root of the product \sqrt{2^{2}\times 70} as the product of square roots \sqrt{2^{2}}\sqrt{70}. Take the square root of 2^{2}.

$$\frac{\sqrt{3}}{2\sqrt{70}}$$

Rationalize the denominator of \frac{\sqrt{3}}{2\sqrt{70}} by multiplying numerator and denominator by \sqrt{70}.

$$\frac{\sqrt{3}\sqrt{70}}{2\left(\sqrt{70}\right)^{2}}$$

The square of \sqrt{70} is 70.

$$\frac{\sqrt{3}\sqrt{70}}{2\times 70}$$

To multiply \sqrt{3} and \sqrt{70}, multiply the numbers under the square root.

$$\frac{\sqrt{210}}{2\times 70}$$

Multiply 2 and 70 to get 140.

$$\frac{\sqrt{210}}{140}$$