Solve (sqrt{6}+sqrt{10}*sqrt{15})*sqrt{3}

$$( \sqrt { 6 } + \sqrt { 10 } \times \sqrt { 15 } ) \times \sqrt { 3 }$$

Evaluate

$$18\sqrt{2}\approx 25.455844123$$

Solution Steps

To multiply \sqrt{10} and \sqrt{15}, multiply the numbers under the square root.

$$\left(\sqrt{6}+\sqrt{150}\right)\sqrt{3}$$

Use the distributive property to multiply \sqrt{6}+\sqrt{150} by \sqrt{3}.

$$\sqrt{6}\sqrt{3}+\sqrt{150}\sqrt{3}$$

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

$$\sqrt{3}\sqrt{2}\sqrt{3}+\sqrt{150}\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$3\sqrt{2}+\sqrt{150}\sqrt{3}$$

Factor 150=3\times 50. Rewrite the square root of the product \sqrt{3\times 50} as the product of square roots \sqrt{3}\sqrt{50}.

$$3\sqrt{2}+\sqrt{3}\sqrt{50}\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$3\sqrt{2}+3\sqrt{50}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$3\sqrt{2}+3\times 5\sqrt{2}$$

Multiply 3 and 5 to get 15.

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

Combine 3\sqrt{2} and 15\sqrt{2} to get 18\sqrt{2}.

$$18\sqrt{2}$$