Solve sqrt{2*98*40*10^-2}

$$\sqrt{ 2 \times 98 \times 40 \times { 10 }^{ -2 } }$$

Evaluate

$$\frac{14\sqrt{10}}{5}\approx 8.854377448$$

Solution Steps

Multiply 2 and 98 to get 196.

$$\sqrt{196\times 40\times 10^{-2}}$$

Multiply 196 and 40 to get 7840.

$$\sqrt{7840\times 10^{-2}}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\sqrt{7840\times \frac{1}{100}}$$

Multiply 7840 and \frac{1}{100} to get \frac{392}{5}.

$$\sqrt{\frac{392}{5}}$$

Rewrite the square root of the division \sqrt{\frac{392}{5}} as the division of square roots \frac{\sqrt{392}}{\sqrt{5}}.

$$\frac{\sqrt{392}}{\sqrt{5}}$$

Factor 392=14^{2}\times 2. Rewrite the square root of the product \sqrt{14^{2}\times 2} as the product of square roots \sqrt{14^{2}}\sqrt{2}. Take the square root of 14^{2}.

$$\frac{14\sqrt{2}}{\sqrt{5}}$$

Rationalize the denominator of \frac{14\sqrt{2}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{14\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{14\sqrt{2}\sqrt{5}}{5}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{14\sqrt{10}}{5}$$