Solve sqrt{75}*sqrt{8}

$$\sqrt { 75 } \times \sqrt { 8 }$$

Evaluate

$$10\sqrt{6}\approx 24.494897428$$

Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$5\sqrt{3}\sqrt{8}$$

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

$$5\sqrt{3}\times 2\sqrt{2}$$

Multiply 5 and 2 to get 10.

$$10\sqrt{3}\sqrt{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$10\sqrt{6}$$