Solve sqrt{12696*10^8/28,574}

$$\sqrt { \frac { 12696 \cdot 10 ^ { 8 } } { 28,574 } }$$

Evaluate

$$\frac{460000\sqrt{42861}}{14287}\approx 6665.733351995$$

Solution Steps

Calculate 10 to the power of 8 and get 100000000.

$$\sqrt{\frac{12696\times 100000000}{28574}}$$

Multiply 12696 and 100000000 to get 1269600000000.

$$\sqrt{\frac{1269600000000}{28574}}$$

Reduce the fraction \frac{1269600000000}{28574} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{634800000000}{14287}}$$

Rewrite the square root of the division \sqrt{\frac{634800000000}{14287}} as the division of square roots \frac{\sqrt{634800000000}}{\sqrt{14287}}.

$$\frac{\sqrt{634800000000}}{\sqrt{14287}}$$

Factor 634800000000=460000^{2}\times 3. Rewrite the square root of the product \sqrt{460000^{2}\times 3} as the product of square roots \sqrt{460000^{2}}\sqrt{3}. Take the square root of 460000^{2}.

$$\frac{460000\sqrt{3}}{\sqrt{14287}}$$

Rationalize the denominator of \frac{460000\sqrt{3}}{\sqrt{14287}} by multiplying numerator and denominator by \sqrt{14287}.

$$\frac{460000\sqrt{3}\sqrt{14287}}{\left(\sqrt{14287}\right)^{2}}$$

The square of \sqrt{14287} is 14287.

$$\frac{460000\sqrt{3}\sqrt{14287}}{14287}$$

To multiply \sqrt{3} and \sqrt{14287}, multiply the numbers under the square root.

$$\frac{460000\sqrt{42861}}{14287}$$