Solve sqrt{2.23*1/5}=

$$\sqrt{ 2.23 \times \frac{ 1 }{ 5 } } =$$

Evaluate

$$\frac{\sqrt{1115}}{50}\approx 0.667832314$$

Solution Steps

Convert decimal number 2.23 to fraction \frac{223}{100}.

$$\sqrt{\frac{223}{100}\times \frac{1}{5}}$$

Multiply \frac{223}{100} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{223\times 1}{100\times 5}}$$

Do the multiplications in the fraction \frac{223\times 1}{100\times 5}.

$$\sqrt{\frac{223}{500}}$$

Rewrite the square root of the division \sqrt{\frac{223}{500}} as the division of square roots \frac{\sqrt{223}}{\sqrt{500}}.

$$\frac{\sqrt{223}}{\sqrt{500}}$$

Factor 500=10^{2}\times 5. Rewrite the square root of the product \sqrt{10^{2}\times 5} as the product of square roots \sqrt{10^{2}}\sqrt{5}. Take the square root of 10^{2}.

$$\frac{\sqrt{223}}{10\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{223}}{10\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{223}\sqrt{5}}{10\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{223}\sqrt{5}}{10\times 5}$$

To multiply \sqrt{223} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{1115}}{10\times 5}$$

Multiply 10 and 5 to get 50.

$$\frac{\sqrt{1115}}{50}$$