Solve sqrt{2*72*16*10^-4/91*10^-32}

$$\sqrt { \frac { 2 \times 72 \times 16 \times 10 ^ { - 4 } } { 91 \times 10 ^ { - 32 } } }$$

Evaluate

$$\frac{4800000000000000\sqrt{91}}{91}\approx 5.031767216 \cdot 10^{14}$$

Solution Steps

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

$$\sqrt{\frac{2\times 16\times 72\times 10^{28}}{91}}$$

Multiply 2 and 16 to get 32.

$$\sqrt{\frac{32\times 72\times 10^{28}}{91}}$$

Multiply 32 and 72 to get 2304.

$$\sqrt{\frac{2304\times 10^{28}}{91}}$$

Calculate 10 to the power of 28 and get 10000000000000000000000000000.

$$\sqrt{\frac{2304\times 10000000000000000000000000000}{91}}$$

Multiply 2304 and 10000000000000000000000000000 to get 23040000000000000000000000000000.

$$\sqrt{\frac{23040000000000000000000000000000}{91}}$$

Rewrite the square root of the division \sqrt{\frac{23040000000000000000000000000000}{91}} as the division of square roots \frac{\sqrt{23040000000000000000000000000000}}{\sqrt{91}}.

$$\frac{\sqrt{23040000000000000000000000000000}}{\sqrt{91}}$$

Calculate the square root of 23040000000000000000000000000000 and get 4800000000000000.

$$\frac{4800000000000000}{\sqrt{91}}$$

Rationalize the denominator of \frac{4800000000000000}{\sqrt{91}} by multiplying numerator and denominator by \sqrt{91}.

$$\frac{4800000000000000\sqrt{91}}{\left(\sqrt{91}\right)^{2}}$$

The square of \sqrt{91} is 91.

$$\frac{4800000000000000\sqrt{91}}{91}$$