Solve sqrt{97*882614*25-84391782/96}

$$\sqrt{ \frac{ 97 \cdot 882614 \cdot 25-84391782 }{ 96 } }$$

Evaluate

$$\frac{\sqrt{192745047}}{3}\approx 4627.754999277$$

Solution Steps

Multiply 97 and 882614 to get 85613558.

$$\sqrt{\frac{85613558\times 25-84391782}{96}}$$

Multiply 85613558 and 25 to get 2140338950.

$$\sqrt{\frac{2140338950-84391782}{96}}$$

Subtract 84391782 from 2140338950 to get 2055947168.

$$\sqrt{\frac{2055947168}{96}}$$

Reduce the fraction \frac{2055947168}{96} to lowest terms by extracting and canceling out 32.

$$\sqrt{\frac{64248349}{3}}$$

Rewrite the square root of the division \sqrt{\frac{64248349}{3}} as the division of square roots \frac{\sqrt{64248349}}{\sqrt{3}}.

$$\frac{\sqrt{64248349}}{\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{64248349}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{64248349}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{64248349}\sqrt{3}}{3}$$

To multiply \sqrt{64248349} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{192745047}}{3}$$