Solve (7sqrt{54}-3sqrt{21}+4sqrt{15})*sqrt{3}

$$( 7 \sqrt { 54 } - 3 \sqrt { 21 } + 4 \sqrt { 15 } ) \times \sqrt { 3 }$$

Evaluate

$$12\sqrt{5}+63\sqrt{2}-9\sqrt{7}\approx 92.11650836$$

Solution Steps

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$\left(7\times 3\sqrt{6}-3\sqrt{21}+4\sqrt{15}\right)\sqrt{3}$$

Multiply 7 and 3 to get 21.

$$\left(21\sqrt{6}-3\sqrt{21}+4\sqrt{15}\right)\sqrt{3}$$

Use the distributive property to multiply 21\sqrt{6}-3\sqrt{21}+4\sqrt{15} by \sqrt{3}.

$$21\sqrt{6}\sqrt{3}-3\sqrt{21}\sqrt{3}+4\sqrt{15}\sqrt{3}$$

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}.

$$21\sqrt{3}\sqrt{2}\sqrt{3}-3\sqrt{21}\sqrt{3}+4\sqrt{15}\sqrt{3}$$

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

$$21\times 3\sqrt{2}-3\sqrt{21}\sqrt{3}+4\sqrt{15}\sqrt{3}$$

Multiply 21 and 3 to get 63.

$$63\sqrt{2}-3\sqrt{21}\sqrt{3}+4\sqrt{15}\sqrt{3}$$

Factor 21=3\times 7. Rewrite the square root of the product \sqrt{3\times 7} as the product of square roots \sqrt{3}\sqrt{7}.

$$63\sqrt{2}-3\sqrt{3}\sqrt{7}\sqrt{3}+4\sqrt{15}\sqrt{3}$$

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

$$63\sqrt{2}-3\times 3\sqrt{7}+4\sqrt{15}\sqrt{3}$$

Multiply -3 and 3 to get -9.

$$63\sqrt{2}-9\sqrt{7}+4\sqrt{15}\sqrt{3}$$

Factor 15=3\times 5. Rewrite the square root of the product \sqrt{3\times 5} as the product of square roots \sqrt{3}\sqrt{5}.

$$63\sqrt{2}-9\sqrt{7}+4\sqrt{3}\sqrt{5}\sqrt{3}$$

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

$$63\sqrt{2}-9\sqrt{7}+4\times 3\sqrt{5}$$

Multiply 4 and 3 to get 12.

$$63\sqrt{2}-9\sqrt{7}+12\sqrt{5}$$