Solve frac{4*sqrt{6}}{sqrt{48}}

$$\frac { 4 \cdot \sqrt { 6 } } { \sqrt { 48 } }$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

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

Cancel out 4 in both numerator and denominator.

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

Rewrite the division of square roots \frac{\sqrt{6}}{\sqrt{3}} as the square root of the division \sqrt{\frac{6}{3}} and perform the division.

$$\sqrt{2}$$