Solve 41sqrt{24}*sqrt{27}

$$41 \sqrt { 24 } \times \sqrt { 27 }$$

Evaluate

$$738\sqrt{2}\approx 1043.689609031$$

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}.

$$41\times 2\sqrt{6}\sqrt{27}$$

Multiply 41 and 2 to get 82.

$$82\sqrt{6}\sqrt{27}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$82\sqrt{6}\times 3\sqrt{3}$$

Multiply 82 and 3 to get 246.

$$246\sqrt{6}\sqrt{3}$$

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}.

$$246\sqrt{3}\sqrt{2}\sqrt{3}$$

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

$$246\times 3\sqrt{2}$$

Multiply 246 and 3 to get 738.

$$738\sqrt{2}$$