Solve sqrt{2*56*9.110^-211.610^-19}

$$\sqrt{ 2 \cdot 56 \cdot 9.1 { 10 }^{ -21 } 1.6 { 10 }^{ -19 } }$$

Evaluate

$$\frac{7\sqrt{13}}{62500000000000000000}\approx 4.038217429 \cdot 10^{-19}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -21 and -19 to get -40.

$$\sqrt{2\times 56\times 9.1\times 10^{-40}\times 1.6}$$

Multiply 2 and 56 to get 112.

$$\sqrt{112\times 9.1\times 10^{-40}\times 1.6}$$

Multiply 112 and 9.1 to get 1019.2.

$$\sqrt{1019.2\times 10^{-40}\times 1.6}$$

Calculate 10 to the power of -40 and get \frac{1}{10000000000000000000000000000000000000000}.

$$\sqrt{1019.2\times \frac{1}{10000000000000000000000000000000000000000}\times 1.6}$$

Multiply 1019.2 and \frac{1}{10000000000000000000000000000000000000000} to get \frac{637}{6250000000000000000000000000000000000000}.

$$\sqrt{\frac{637}{6250000000000000000000000000000000000000}\times 1.6}$$

Multiply \frac{637}{6250000000000000000000000000000000000000} and 1.6 to get \frac{637}{3906250000000000000000000000000000000000}.

$$\sqrt{\frac{637}{3906250000000000000000000000000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{637}{3906250000000000000000000000000000000000}} as the division of square roots \frac{\sqrt{637}}{\sqrt{3906250000000000000000000000000000000000}}.

$$\frac{\sqrt{637}}{\sqrt{3906250000000000000000000000000000000000}}$$

Factor 637=7^{2}\times 13. Rewrite the square root of the product \sqrt{7^{2}\times 13} as the product of square roots \sqrt{7^{2}}\sqrt{13}. Take the square root of 7^{2}.

$$\frac{7\sqrt{13}}{\sqrt{3906250000000000000000000000000000000000}}$$

Calculate the square root of 3906250000000000000000000000000000000000 and get 62500000000000000000.

$$\frac{7\sqrt{13}}{62500000000000000000}$$