Solve 4sqrt{98}*sqrt{96}

$$4 \sqrt { 98 } \times \sqrt { 96 }$$

Evaluate

$$224\sqrt{3}\approx 387.979380895$$

Solution Steps

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$4\times 7\sqrt{2}\sqrt{96}$$

Multiply 4 and 7 to get 28.

$$28\sqrt{2}\sqrt{96}$$

Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.

$$28\sqrt{2}\times 4\sqrt{6}$$

Multiply 28 and 4 to get 112.

$$112\sqrt{2}\sqrt{6}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$112\sqrt{2}\sqrt{2}\sqrt{3}$$

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

$$112\times 2\sqrt{3}$$

Multiply 112 and 2 to get 224.

$$224\sqrt{3}$$