Solve sqrt{1-25*21/28^2}

$$\sqrt { 1 - \frac { 25 \times 21 } { 28 ^ { 2 } } }$$

Evaluate

$$\frac{\sqrt{259}}{28}\approx 0.574767034$$

Solution Steps

Multiply 25 and 21 to get 525.

$$\sqrt{1-\frac{525}{28^{2}}}$$

Calculate 28 to the power of 2 and get 784.

$$\sqrt{1-\frac{525}{784}}$$

Reduce the fraction \frac{525}{784} to lowest terms by extracting and canceling out 7.

$$\sqrt{1-\frac{75}{112}}$$

Convert 1 to fraction \frac{112}{112}.

$$\sqrt{\frac{112}{112}-\frac{75}{112}}$$

Since \frac{112}{112} and \frac{75}{112} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{112-75}{112}}$$

Subtract 75 from 112 to get 37.

$$\sqrt{\frac{37}{112}}$$

Rewrite the square root of the division \sqrt{\frac{37}{112}} as the division of square roots \frac{\sqrt{37}}{\sqrt{112}}.

$$\frac{\sqrt{37}}{\sqrt{112}}$$

Factor 112=4^{2}\times 7. Rewrite the square root of the product \sqrt{4^{2}\times 7} as the product of square roots \sqrt{4^{2}}\sqrt{7}. Take the square root of 4^{2}.

$$\frac{\sqrt{37}}{4\sqrt{7}}$$

Rationalize the denominator of \frac{\sqrt{37}}{4\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{\sqrt{37}\sqrt{7}}{4\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{\sqrt{37}\sqrt{7}}{4\times 7}$$

To multiply \sqrt{37} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{\sqrt{259}}{4\times 7}$$

Multiply 4 and 7 to get 28.

$$\frac{\sqrt{259}}{28}$$