Solve sqrt{24}*2sqrt{18}

$$\sqrt { 24 } \times 2 \sqrt { 18 }$$

Evaluate

$$24\sqrt{3}\approx 41.569219382$$

Solution Steps

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}.

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

Multiply 2 and 2 to get 4.

$$4\sqrt{6}\sqrt{18}$$

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}.

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

Multiply 4 and 3 to get 12.

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

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}.

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

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

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

Multiply 12 and 2 to get 24.

$$24\sqrt{3}$$