Solve frac{400sqrt{6}}{100sqrt{3}}

$$\frac { 400 \sqrt { 6 } } { 100 \sqrt { 3 } }$$

Evaluate

$$4\sqrt{2}\approx 5.656854249$$

Solution Steps

Cancel out 100 in both numerator and denominator.

$$\frac{4\sqrt{6}}{\sqrt{3}}$$

Rationalize the denominator of \frac{4\sqrt{6}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{4\sqrt{6}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{4\sqrt{6}\sqrt{3}}{3}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$\frac{4\sqrt{3}\sqrt{2}\sqrt{3}}{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{4\times 3\sqrt{2}}{3}$$

Cancel out 3 and 3.

$$4\sqrt{2}$$