Solve sqrt{54}sqrt{96}sqrt{24}

$$\sqrt { 54 } \sqrt { 96 } \sqrt { 24 }$$

Evaluate

$$144\sqrt{6}\approx 352.726522961$$

Solution Steps

Factor 96=24\times 4. Rewrite the square root of the product \sqrt{24\times 4} as the product of square roots \sqrt{24}\sqrt{4}.

$$\sqrt{54}\sqrt{24}\sqrt{4}\sqrt{24}$$

Multiply \sqrt{24} and \sqrt{24} to get 24.

$$\sqrt{54}\times 24\sqrt{4}$$

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}.

$$3\sqrt{6}\times 24\sqrt{4}$$

Multiply 3 and 24 to get 72.

$$72\sqrt{6}\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$72\sqrt{6}\times 2$$

Multiply 72 and 2 to get 144.

$$144\sqrt{6}$$