Solve sqrt{2*16*10^-19*500/91*10^-31}

$$\sqrt{ \frac{ 2 \cdot 16 \times { 10 }^{ -19 } \times 500 }{ 91 \times { 10 }^{ -31 } } }$$

Evaluate

$$\frac{40000000\sqrt{910}}{91}\approx 13259870.882635918$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\sqrt{\frac{2\times 16\times 500\times 10^{12}}{91}}$$

Multiply 2 and 16 to get 32.

$$\sqrt{\frac{32\times 500\times 10^{12}}{91}}$$

Multiply 32 and 500 to get 16000.

$$\sqrt{\frac{16000\times 10^{12}}{91}}$$

Calculate 10 to the power of 12 and get 1000000000000.

$$\sqrt{\frac{16000\times 1000000000000}{91}}$$

Multiply 16000 and 1000000000000 to get 16000000000000000.

$$\sqrt{\frac{16000000000000000}{91}}$$

Rewrite the square root of the division \sqrt{\frac{16000000000000000}{91}} as the division of square roots \frac{\sqrt{16000000000000000}}{\sqrt{91}}.

$$\frac{\sqrt{16000000000000000}}{\sqrt{91}}$$

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}.

$$\frac{40000000\sqrt{10}}{\sqrt{91}}$$

Rationalize the denominator of \frac{40000000\sqrt{10}}{\sqrt{91}} by multiplying numerator and denominator by \sqrt{91}.

$$\frac{40000000\sqrt{10}\sqrt{91}}{\left(\sqrt{91}\right)^{2}}$$

The square of \sqrt{91} is 91.

$$\frac{40000000\sqrt{10}\sqrt{91}}{91}$$

To multiply \sqrt{10} and \sqrt{91}, multiply the numbers under the square root.

$$\frac{40000000\sqrt{910}}{91}$$