Solve sqrt{2}*sqrt{100}

$$\sqrt { 2 } \times \sqrt { 100 }$$

Evaluate

$$10\sqrt{2}\approx 14.142135624$$

Solution Steps

Factor 100=2\times 50. Rewrite the square root of the product \sqrt{2\times 50} as the product of square roots \sqrt{2}\sqrt{50}.

$$\sqrt{2}\sqrt{2}\sqrt{50}$$

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

$$2\sqrt{50}$$

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}.

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

Multiply 2 and 5 to get 10.

$$10\sqrt{2}$$