Solve frac{sqrt{24}+sqrt{54}-sqrt{150}}{sqrt{108}}

$$\frac { \sqrt { 24 } + \sqrt { 54 } - \sqrt { 150 } } { \sqrt { 108 } }$$

Evaluate

$$0$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\frac{2\sqrt{6}+\sqrt{54}-\sqrt{150}}{\sqrt{108}}$$

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$\frac{2\sqrt{6}+3\sqrt{6}-\sqrt{150}}{\sqrt{108}}$$

Combine 2\sqrt{6} and 3\sqrt{6} to get 5\sqrt{6}.

$$\frac{5\sqrt{6}-\sqrt{150}}{\sqrt{108}}$$

Factor 150=5^{2}\times 6. Rewrite the square root of the product \sqrt{5^{2}\times 6} as the product of square roots \sqrt{5^{2}}\sqrt{6}. Take the square root of 5^{2}.

$$\frac{5\sqrt{6}-5\sqrt{6}}{\sqrt{108}}$$

Combine 5\sqrt{6} and -5\sqrt{6} to get 0.

$$\frac{0}{\sqrt{108}}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$\frac{0}{6\sqrt{3}}$$

Zero divided by any non-zero term gives zero.

$$0$$

Factor

$$0$$