Solve 4sqrt{2}-3sqrt{2}*sqrt{24}

$$4 \sqrt{ 2 } -3 \sqrt{ 2 } \times \sqrt{ 24 }$$

Evaluate

$$4\left(\sqrt{2}-3\sqrt{3}\right)\approx -15.127755441$$

Solution Steps

Factor 24=2\times 12. Rewrite the square root of the product \sqrt{2\times 12} as the product of square roots \sqrt{2}\sqrt{12}.

$$4\sqrt{2}-3\sqrt{2}\sqrt{2}\sqrt{12}$$

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

$$4\sqrt{2}-3\times 2\sqrt{12}$$

Multiply 3 and 2 to get 6.

$$4\sqrt{2}-6\sqrt{12}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

Multiply 6 and 2 to get 12.

$$4\sqrt{2}-12\sqrt{3}$$

Factor

$$4 {(\sqrt{2} - 3 \sqrt{3})} = -15.127755441$$