Solve 3sqrt{392}*3sqrt{448}

$$3 \sqrt { 392 } \times 3 \sqrt { 448 }$$

Evaluate

$$1008\sqrt{14}\approx 3771.590645868$$

Solution Steps

Multiply 3 and 3 to get 9.

$$9\sqrt{392}\sqrt{448}$$

Factor 392=14^{2}\times 2. Rewrite the square root of the product \sqrt{14^{2}\times 2} as the product of square roots \sqrt{14^{2}}\sqrt{2}. Take the square root of 14^{2}.

$$9\times 14\sqrt{2}\sqrt{448}$$

Multiply 9 and 14 to get 126.

$$126\sqrt{2}\sqrt{448}$$

Factor 448=8^{2}\times 7. Rewrite the square root of the product \sqrt{8^{2}\times 7} as the product of square roots \sqrt{8^{2}}\sqrt{7}. Take the square root of 8^{2}.

$$126\sqrt{2}\times 8\sqrt{7}$$

Multiply 126 and 8 to get 1008.

$$1008\sqrt{2}\sqrt{7}$$

To multiply \sqrt{2} and \sqrt{7}, multiply the numbers under the square root.

$$1008\sqrt{14}$$