Solve frac{2sqrt{2}}{sqrt{32}-sqrt{18}}2232-18

$$\frac { 2 \sqrt { 2 } } { \sqrt { 32 } - \sqrt { 18 } } 2232 - 18$$

Evaluate

$$4446$$

Solution Steps

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$2232\times \frac{2\sqrt{2}}{4\sqrt{2}-\sqrt{18}}-18$$

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}.

$$2232\times \frac{2\sqrt{2}}{4\sqrt{2}-3\sqrt{2}}-18$$

Combine 4\sqrt{2} and -3\sqrt{2} to get \sqrt{2}.

$$2232\times \frac{2\sqrt{2}}{\sqrt{2}}-18$$

Rationalize the denominator of \frac{2\sqrt{2}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$2232\times \frac{2\sqrt{2}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-18$$

The square of \sqrt{2} is 2.

$$2232\times \frac{2\sqrt{2}\sqrt{2}}{2}-18$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$2232\times \frac{2\times 2}{2}-18$$

Multiply 2 and 2 to get 4.

$$2232\times \frac{4}{2}-18$$

Divide 4 by 2 to get 2.

$$2232\times 2-18$$

Multiply 2232 and 2 to get 4464.

$$4464-18$$

Subtract 18 from 4464 to get 4446.

$$4446$$

Factor

$$2\times 3^{2}\times 13\times 19$$