Solve sqrt{1/20-1[112-(38)^2/20}

$$\sqrt { \frac { 1 } { 20 - 1 } [ 112 - \frac { ( 38 ) ^ { 2 } } { 20 } }$$

Evaluate

$$\frac{\sqrt{18905}}{95}\approx 1.447320573$$

Solution Steps

Subtract 1 from 20 to get 19.

$$\sqrt{\frac{1}{19}\left(112-\frac{38^{2}}{20}\right)}$$

Calculate 38 to the power of 2 and get 1444.

$$\sqrt{\frac{1}{19}\left(112-\frac{1444}{20}\right)}$$

Reduce the fraction \frac{1444}{20} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{1}{19}\left(112-\frac{361}{5}\right)}$$

Convert 112 to fraction \frac{560}{5}.

$$\sqrt{\frac{1}{19}\left(\frac{560}{5}-\frac{361}{5}\right)}$$

Since \frac{560}{5} and \frac{361}{5} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{1}{19}\times \frac{560-361}{5}}$$

Subtract 361 from 560 to get 199.

$$\sqrt{\frac{1}{19}\times \frac{199}{5}}$$

Multiply \frac{1}{19} times \frac{199}{5} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{1\times 199}{19\times 5}}$$

Do the multiplications in the fraction \frac{1\times 199}{19\times 5}.

$$\sqrt{\frac{199}{95}}$$

Rewrite the square root of the division \sqrt{\frac{199}{95}} as the division of square roots \frac{\sqrt{199}}{\sqrt{95}}.

$$\frac{\sqrt{199}}{\sqrt{95}}$$

Rationalize the denominator of \frac{\sqrt{199}}{\sqrt{95}} by multiplying numerator and denominator by \sqrt{95}.

$$\frac{\sqrt{199}\sqrt{95}}{\left(\sqrt{95}\right)^{2}}$$

The square of \sqrt{95} is 95.

$$\frac{\sqrt{199}\sqrt{95}}{95}$$

To multiply \sqrt{199} and \sqrt{95}, multiply the numbers under the square root.

$$\frac{\sqrt{18905}}{95}$$