Solve =sqrt{12343/2361}

$$= \sqrt{ 12 \frac { 343 } { 2361 } }$$

Evaluate

$$\frac{5\sqrt{2708067}}{2361}\approx 3.485007521$$

Solution Steps

Multiply 12 and 2361 to get 28332.

$$\sqrt{\frac{28332+343}{2361}}$$

Add 28332 and 343 to get 28675.

$$\sqrt{\frac{28675}{2361}}$$

Rewrite the square root of the division \sqrt{\frac{28675}{2361}} as the division of square roots \frac{\sqrt{28675}}{\sqrt{2361}}.

$$\frac{\sqrt{28675}}{\sqrt{2361}}$$

Factor 28675=5^{2}\times 1147. Rewrite the square root of the product \sqrt{5^{2}\times 1147} as the product of square roots \sqrt{5^{2}}\sqrt{1147}. Take the square root of 5^{2}.

$$\frac{5\sqrt{1147}}{\sqrt{2361}}$$

Rationalize the denominator of \frac{5\sqrt{1147}}{\sqrt{2361}} by multiplying numerator and denominator by \sqrt{2361}.

$$\frac{5\sqrt{1147}\sqrt{2361}}{\left(\sqrt{2361}\right)^{2}}$$

The square of \sqrt{2361} is 2361.

$$\frac{5\sqrt{1147}\sqrt{2361}}{2361}$$

To multiply \sqrt{1147} and \sqrt{2361}, multiply the numbers under the square root.

$$\frac{5\sqrt{2708067}}{2361}$$