Solve sqrt{1.05*10^-14/56}

$$\sqrt{ \frac{ 1.05 \times { 10 }^{ -14 } }{ 56 } }$$

Evaluate

$$\frac{\sqrt{30}}{400000000}\approx 0.000000014$$

Solution Steps

Calculate 10 to the power of -14 and get \frac{1}{100000000000000}.

$$\sqrt{\frac{1.05\times \frac{1}{100000000000000}}{56}}$$

Multiply 1.05 and \frac{1}{100000000000000} to get \frac{21}{2000000000000000}.

$$\sqrt{\frac{\frac{21}{2000000000000000}}{56}}$$

Express \frac{\frac{21}{2000000000000000}}{56} as a single fraction.

$$\sqrt{\frac{21}{2000000000000000\times 56}}$$

Multiply 2000000000000000 and 56 to get 112000000000000000.

$$\sqrt{\frac{21}{112000000000000000}}$$

Reduce the fraction \frac{21}{112000000000000000} to lowest terms by extracting and canceling out 7.

$$\sqrt{\frac{3}{16000000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{3}{16000000000000000}} as the division of square roots \frac{\sqrt{3}}{\sqrt{16000000000000000}}.

$$\frac{\sqrt{3}}{\sqrt{16000000000000000}}$$

Factor 16000000000000000=40000000^{2}\times 10. Rewrite the square root of the product \sqrt{40000000^{2}\times 10} as the product of square roots \sqrt{40000000^{2}}\sqrt{10}. Take the square root of 40000000^{2}.

$$\frac{\sqrt{3}}{40000000\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{3}}{40000000\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{3}\sqrt{10}}{40000000\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{3}\sqrt{10}}{40000000\times 10}$$

To multiply \sqrt{3} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{30}}{40000000\times 10}$$

Multiply 40000000 and 10 to get 400000000.

$$\frac{\sqrt{30}}{400000000}$$