Solve frac{sqrt{18}}{5sqrt{18}+3sqrt{72}-2sqrt{162}}

$$\frac { \sqrt { 18 } } { 5 \sqrt { 18 } + 3 \sqrt { 72 } - 2 \sqrt { 162 } }$$

Evaluate

$$\frac{1}{5}=0.2$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{3\sqrt{2}}{5\sqrt{18}+3\sqrt{72}-2\sqrt{162}}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{3\sqrt{2}}{5\times 3\sqrt{2}+3\sqrt{72}-2\sqrt{162}}$$

Multiply 5 and 3 to get 15.

$$\frac{3\sqrt{2}}{15\sqrt{2}+3\sqrt{72}-2\sqrt{162}}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$\frac{3\sqrt{2}}{15\sqrt{2}+3\times 6\sqrt{2}-2\sqrt{162}}$$

Multiply 3 and 6 to get 18.

$$\frac{3\sqrt{2}}{15\sqrt{2}+18\sqrt{2}-2\sqrt{162}}$$

Combine 15\sqrt{2} and 18\sqrt{2} to get 33\sqrt{2}.

$$\frac{3\sqrt{2}}{33\sqrt{2}-2\sqrt{162}}$$

Factor 162=9^{2}\times 2. Rewrite the square root of the product \sqrt{9^{2}\times 2} as the product of square roots \sqrt{9^{2}}\sqrt{2}. Take the square root of 9^{2}.

$$\frac{3\sqrt{2}}{33\sqrt{2}-2\times 9\sqrt{2}}$$

Multiply -2 and 9 to get -18.

$$\frac{3\sqrt{2}}{33\sqrt{2}-18\sqrt{2}}$$

Combine 33\sqrt{2} and -18\sqrt{2} to get 15\sqrt{2}.

$$\frac{3\sqrt{2}}{15\sqrt{2}}$$

Cancel out 3\sqrt{2} in both numerator and denominator.

$$\frac{1}{5}$$

Factor

$$\frac{1}{5} = 0.2$$