Solve sqrt{50}*sqrt{45}

$$\sqrt { 50 } \times \sqrt { 45 }$$

Evaluate

$$15\sqrt{10}\approx 47.434164903$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$5\sqrt{2}\sqrt{45}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

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

Multiply 5 and 3 to get 15.

$$15\sqrt{2}\sqrt{5}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$15\sqrt{10}$$