Solve sqrt{12}*4sqrt{54}

$$\sqrt { 12 } \times 4 \sqrt { 54 }$$

Evaluate

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

Solution Steps

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}.

$$4\times 2\sqrt{3}\sqrt{54}$$

Multiply 4 and 2 to get 8.

$$8\sqrt{3}\sqrt{54}$$

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}.

$$8\sqrt{3}\times 3\sqrt{6}$$

Multiply 8 and 3 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.

$$72\sqrt{2}$$