Solve sqrt{0.97*10^-3/0.0115*10^-6}=

$$\sqrt { \frac { 0.97 \times 10 ^ { - 3 } } { 0.0115 \times 10 ^ { - 6 } } } =$$

Evaluate

$$\frac{100\sqrt{4462}}{23}\approx 290.426972038$$

Solution Steps

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

$$\sqrt{\frac{0.97\times 10^{3}}{0.0115}}$$

Calculate 10 to the power of 3 and get 1000.

$$\sqrt{\frac{0.97\times 1000}{0.0115}}$$

Multiply 0.97 and 1000 to get 970.

$$\sqrt{\frac{970}{0.0115}}$$

Expand \frac{970}{0.0115} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{9700000}{115}}$$

Reduce the fraction \frac{9700000}{115} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{1940000}{23}}$$

Rewrite the square root of the division \sqrt{\frac{1940000}{23}} as the division of square roots \frac{\sqrt{1940000}}{\sqrt{23}}.

$$\frac{\sqrt{1940000}}{\sqrt{23}}$$

Factor 1940000=100^{2}\times 194. Rewrite the square root of the product \sqrt{100^{2}\times 194} as the product of square roots \sqrt{100^{2}}\sqrt{194}. Take the square root of 100^{2}.

$$\frac{100\sqrt{194}}{\sqrt{23}}$$

Rationalize the denominator of \frac{100\sqrt{194}}{\sqrt{23}} by multiplying numerator and denominator by \sqrt{23}.

$$\frac{100\sqrt{194}\sqrt{23}}{\left(\sqrt{23}\right)^{2}}$$

The square of \sqrt{23} is 23.

$$\frac{100\sqrt{194}\sqrt{23}}{23}$$

To multiply \sqrt{194} and \sqrt{23}, multiply the numbers under the square root.

$$\frac{100\sqrt{4462}}{23}$$