Solve 2sqrt{27}*sqrt{96}

$$2 \sqrt { 27 } \times \sqrt { 96 }$$

Evaluate

$$72\sqrt{2}\approx 101.823376491$$

Solution Steps

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}.

$$2\times 3\sqrt{3}\sqrt{96}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{3}\sqrt{96}$$

Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.

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

Multiply 6 and 4 to get 24.

$$24\sqrt{3}\sqrt{6}$$

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}.

$$24\sqrt{3}\sqrt{3}\sqrt{2}$$

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

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

Multiply 24 and 3 to get 72.

$$72\sqrt{2}$$