Solve sqrt{54}*4sqrt{48}

$$\sqrt { 54 } \times 4 \sqrt { 48 }$$

Evaluate

$$144\sqrt{2}\approx 203.646752982$$

Solution Steps

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}.

$$4\times 3\sqrt{6}\sqrt{48}$$

Multiply 4 and 3 to get 12.

$$12\sqrt{6}\sqrt{48}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$12\sqrt{6}\times 4\sqrt{3}$$

Multiply 12 and 4 to get 48.

$$48\sqrt{6}\sqrt{3}$$

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}.

$$48\sqrt{3}\sqrt{2}\sqrt{3}$$

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

$$48\times 3\sqrt{2}$$

Multiply 48 and 3 to get 144.

$$144\sqrt{2}$$