Solve sqrt{0.075*1div7}

$$\sqrt{ 0.075 \times 1 \div 7 }$$

Evaluate

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

Solution Steps

Multiply 0.075 and 1 to get 0.075.

$$\sqrt{\frac{0.075}{7}}$$

Expand \frac{0.075}{7} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{75}{7000}}$$

Reduce the fraction \frac{75}{7000} to lowest terms by extracting and canceling out 25.

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

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.

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