Solve 1/2*sqrt{29}*sqrt{37}*sqrt{1-17^2/1073}

$$\frac { 1 } { 2 } \cdot \sqrt { 29 } \cdot \sqrt { 37 } \cdot \sqrt { 1 - \frac { 17 ^ { 2 } } { 1073 } }$$

Evaluate

$$14$$

Solution Steps

Calculate 17 to the power of 2 and get 289.

$$\frac{1}{2}\sqrt{29}\sqrt{37}\sqrt{1-\frac{289}{1073}}$$

Convert 1 to fraction \frac{1073}{1073}.

$$\frac{1}{2}\sqrt{29}\sqrt{37}\sqrt{\frac{1073}{1073}-\frac{289}{1073}}$$

Since \frac{1073}{1073} and \frac{289}{1073} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\sqrt{29}\sqrt{37}\sqrt{\frac{1073-289}{1073}}$$

Subtract 289 from 1073 to get 784.

$$\frac{1}{2}\sqrt{29}\sqrt{37}\sqrt{\frac{784}{1073}}$$

Rewrite the square root of the division \sqrt{\frac{784}{1073}} as the division of square roots \frac{\sqrt{784}}{\sqrt{1073}}.

$$\frac{1}{2}\sqrt{29}\sqrt{37}\times \frac{\sqrt{784}}{\sqrt{1073}}$$

Calculate the square root of 784 and get 28.

$$\frac{1}{2}\sqrt{29}\sqrt{37}\times \frac{28}{\sqrt{1073}}$$

Rationalize the denominator of \frac{28}{\sqrt{1073}} by multiplying numerator and denominator by \sqrt{1073}.

$$\frac{1}{2}\sqrt{29}\sqrt{37}\times \frac{28\sqrt{1073}}{\left(\sqrt{1073}\right)^{2}}$$

The square of \sqrt{1073} is 1073.

$$\frac{1}{2}\sqrt{29}\sqrt{37}\times \frac{28\sqrt{1073}}{1073}$$

Multiply \frac{1}{2} times \frac{28\sqrt{1073}}{1073} by multiplying numerator times numerator and denominator times denominator.

$$\frac{28\sqrt{1073}}{2\times 1073}\sqrt{29}\sqrt{37}$$

Cancel out 2 in both numerator and denominator.

$$\frac{14\sqrt{1073}}{1073}\sqrt{29}\sqrt{37}$$

To multiply \sqrt{29} and \sqrt{37}, multiply the numbers under the square root.

$$\frac{14\sqrt{1073}}{1073}\sqrt{1073}$$

Express \frac{14\sqrt{1073}}{1073}\sqrt{1073} as a single fraction.

$$\frac{14\sqrt{1073}\sqrt{1073}}{1073}$$

Multiply \sqrt{1073} and \sqrt{1073} to get 1073.

$$\frac{14\times 1073}{1073}$$

Cancel out 1073 and 1073.

$$14$$

Factor

$$2\times 7$$