Solve sqrt{24}sqrt{2}7

$$\sqrt{ 24 } \sqrt{ 2 } 7$$

Evaluate

$$28\sqrt{3}\approx 48.497422612$$

Solution Steps

Factor 24=2\times 12. Rewrite the square root of the product \sqrt{2\times 12} as the product of square roots \sqrt{2}\sqrt{12}.

$$7\sqrt{2}\sqrt{12}\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$7\times 2\sqrt{12}$$

Multiply 7 and 2 to get 14.

$$14\sqrt{12}$$

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}.

$$14\times 2\sqrt{3}$$

Multiply 14 and 2 to get 28.

$$28\sqrt{3}$$