Solve 2/5*sqrt{75}+sqrt{24}*3sqrt{18}

$$\frac { 2 } { 5 } \times \sqrt { 75 } + \sqrt { 24 } \times 3 \sqrt { 18 }$$

Evaluate

$$38\sqrt{3}\approx 65.817930688$$

Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$\frac{2}{5}\times 5\sqrt{3}+3\sqrt{24}\sqrt{18}$$

Cancel out 5 and 5.

$$2\sqrt{3}+3\sqrt{24}\sqrt{18}$$

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}.

$$2\sqrt{3}+3\times 2\sqrt{6}\sqrt{18}$$

Multiply 3 and 2 to get 6.

$$2\sqrt{3}+6\sqrt{6}\sqrt{18}$$

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}.

$$2\sqrt{3}+6\sqrt{6}\times 3\sqrt{2}$$

Multiply 6 and 3 to get 18.

$$2\sqrt{3}+18\sqrt{6}\sqrt{2}$$

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}.

$$2\sqrt{3}+18\sqrt{2}\sqrt{3}\sqrt{2}$$

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

$$2\sqrt{3}+18\times 2\sqrt{3}$$

Multiply 18 and 2 to get 36.

$$2\sqrt{3}+36\sqrt{3}$$

Combine 2\sqrt{3} and 36\sqrt{3} to get 38\sqrt{3}.

$$38\sqrt{3}$$