Solve =sqrt{1/20-1[55-(15)^2/20]}

$$= \sqrt { \frac { 1 } { 20 - 1 } [ 55 - \frac { ( 15 ) ^ { 2 } } { 20 } ] }$$

Evaluate

$$\frac{5\sqrt{133}}{38}\approx 1.517442447$$

Solution Steps

Subtract 1 from 20 to get 19.

$$\sqrt{\frac{1}{19}\left(55-\frac{15^{2}}{20}\right)}$$

Calculate 15 to the power of 2 and get 225.

$$\sqrt{\frac{1}{19}\left(55-\frac{225}{20}\right)}$$

Reduce the fraction \frac{225}{20} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{1}{19}\left(55-\frac{45}{4}\right)}$$

Convert 55 to fraction \frac{220}{4}.

$$\sqrt{\frac{1}{19}\left(\frac{220}{4}-\frac{45}{4}\right)}$$

Since \frac{220}{4} and \frac{45}{4} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{1}{19}\times \frac{220-45}{4}}$$

Subtract 45 from 220 to get 175.

$$\sqrt{\frac{1}{19}\times \frac{175}{4}}$$

Multiply \frac{1}{19} times \frac{175}{4} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{1\times 175}{19\times 4}}$$

Do the multiplications in the fraction \frac{1\times 175}{19\times 4}.

$$\sqrt{\frac{175}{76}}$$

Rewrite the square root of the division \sqrt{\frac{175}{76}} as the division of square roots \frac{\sqrt{175}}{\sqrt{76}}.

$$\frac{\sqrt{175}}{\sqrt{76}}$$

Factor 175=5^{2}\times 7. Rewrite the square root of the product \sqrt{5^{2}\times 7} as the product of square roots \sqrt{5^{2}}\sqrt{7}. Take the square root of 5^{2}.

$$\frac{5\sqrt{7}}{\sqrt{76}}$$

Factor 76=2^{2}\times 19. Rewrite the square root of the product \sqrt{2^{2}\times 19} as the product of square roots \sqrt{2^{2}}\sqrt{19}. Take the square root of 2^{2}.

$$\frac{5\sqrt{7}}{2\sqrt{19}}$$

Rationalize the denominator of \frac{5\sqrt{7}}{2\sqrt{19}} by multiplying numerator and denominator by \sqrt{19}.

$$\frac{5\sqrt{7}\sqrt{19}}{2\left(\sqrt{19}\right)^{2}}$$

The square of \sqrt{19} is 19.

$$\frac{5\sqrt{7}\sqrt{19}}{2\times 19}$$

To multiply \sqrt{7} and \sqrt{19}, multiply the numbers under the square root.

$$\frac{5\sqrt{133}}{2\times 19}$$

Multiply 2 and 19 to get 38.

$$\frac{5\sqrt{133}}{38}$$