Solve sqrt{2.23(1/5+(150-152)^2/10})

$$\sqrt { 2.23 ( \frac { 1 } { 5 } + \frac { ( 150 - 152 ) ^ { 2 } } { 10 } } )$$

Evaluate

$$\frac{\sqrt{3345}}{50}\approx 1.156719499$$

Solution Steps

Subtract 152 from 150 to get -2.

$$\sqrt{2.23\left(\frac{1}{5}+\frac{\left(-2\right)^{2}}{10}\right)}$$

Calculate -2 to the power of 2 and get 4.

$$\sqrt{2.23\left(\frac{1}{5}+\frac{4}{10}\right)}$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\sqrt{2.23\left(\frac{1}{5}+\frac{2}{5}\right)}$$

Add \frac{1}{5} and \frac{2}{5} to get \frac{3}{5}.

$$\sqrt{2.23\times \frac{3}{5}}$$

Multiply 2.23 and \frac{3}{5} to get \frac{669}{500}.

$$\sqrt{\frac{669}{500}}$$

Rewrite the square root of the division \sqrt{\frac{669}{500}} as the division of square roots \frac{\sqrt{669}}{\sqrt{500}}.

$$\frac{\sqrt{669}}{\sqrt{500}}$$

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}.

$$\frac{\sqrt{669}}{10\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{669}}{10\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{669}\sqrt{5}}{10\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{669}\sqrt{5}}{10\times 5}$$

To multiply \sqrt{669} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{3345}}{10\times 5}$$

Multiply 10 and 5 to get 50.

$$\frac{\sqrt{3345}}{50}$$