Solve sqrt{667*10^-11*199*10^30/459*10^10}

$$\sqrt { \frac { 667 \times 10 ^ { - 11 } \times 199 \times 10 ^ { 30 } } { 459 \times 10 ^ { 10 } } }$$

Evaluate

$$\frac{10000\sqrt{67693830}}{153}\approx 537753.334938495$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -11 and 30 to get 19.

$$\sqrt{\frac{667\times 10^{19}\times 199}{459\times 10^{10}}}$$

Cancel out 10^{10} in both numerator and denominator.

$$\sqrt{\frac{199\times 667\times 10^{9}}{459}}$$

Multiply 199 and 667 to get 132733.

$$\sqrt{\frac{132733\times 10^{9}}{459}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$\sqrt{\frac{132733\times 1000000000}{459}}$$

Multiply 132733 and 1000000000 to get 132733000000000.

$$\sqrt{\frac{132733000000000}{459}}$$

Rewrite the square root of the division \sqrt{\frac{132733000000000}{459}} as the division of square roots \frac{\sqrt{132733000000000}}{\sqrt{459}}.

$$\frac{\sqrt{132733000000000}}{\sqrt{459}}$$

Factor 132733000000000=10000^{2}\times 1327330. Rewrite the square root of the product \sqrt{10000^{2}\times 1327330} as the product of square roots \sqrt{10000^{2}}\sqrt{1327330}. Take the square root of 10000^{2}.

$$\frac{10000\sqrt{1327330}}{\sqrt{459}}$$

Factor 459=3^{2}\times 51. Rewrite the square root of the product \sqrt{3^{2}\times 51} as the product of square roots \sqrt{3^{2}}\sqrt{51}. Take the square root of 3^{2}.

$$\frac{10000\sqrt{1327330}}{3\sqrt{51}}$$

Rationalize the denominator of \frac{10000\sqrt{1327330}}{3\sqrt{51}} by multiplying numerator and denominator by \sqrt{51}.

$$\frac{10000\sqrt{1327330}\sqrt{51}}{3\left(\sqrt{51}\right)^{2}}$$

The square of \sqrt{51} is 51.

$$\frac{10000\sqrt{1327330}\sqrt{51}}{3\times 51}$$

To multiply \sqrt{1327330} and \sqrt{51}, multiply the numbers under the square root.

$$\frac{10000\sqrt{67693830}}{3\times 51}$$

Multiply 3 and 51 to get 153.

$$\frac{10000\sqrt{67693830}}{153}$$