Solve (sqrt{150}-sqrt{24}):(2sqrt{8}-3sqrt{2})=

$$( \sqrt { 150 } - \sqrt { 24 } ) : ( 2 \sqrt { 8 } - 3 \sqrt { 2 } ) =$$

Evaluate

$$3\sqrt{3}\approx 5.196152423$$

Solution Steps

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}.

$$\frac{5\sqrt{6}-\sqrt{24}}{2\sqrt{8}-3\sqrt{2}}$$

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}.

$$\frac{5\sqrt{6}-2\sqrt{6}}{2\sqrt{8}-3\sqrt{2}}$$

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

$$\frac{3\sqrt{6}}{2\sqrt{8}-3\sqrt{2}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{3\sqrt{6}}{2\times 2\sqrt{2}-3\sqrt{2}}$$

Multiply 2 and 2 to get 4.

$$\frac{3\sqrt{6}}{4\sqrt{2}-3\sqrt{2}}$$

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

$$\frac{3\sqrt{6}}{\sqrt{2}}$$

Rationalize the denominator of \frac{3\sqrt{6}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{6}\sqrt{2}}{2}$$

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

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

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

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

Cancel out 2 and 2.

$$3\sqrt{3}$$