Solve (sqrt{50}-151)sqrt{51}=

$$( \sqrt { 50 } - 151 ) \sqrt { 51 } =$$

Evaluate

$$\sqrt{51}\left(5\sqrt{2}-151\right)\approx -1027.858168018$$

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}.

$$\left(5\sqrt{2}-151\right)\sqrt{51}$$

Use the distributive property to multiply 5\sqrt{2}-151 by \sqrt{51}.

$$5\sqrt{2}\sqrt{51}-151\sqrt{51}$$

To multiply \sqrt{2} and \sqrt{51}, multiply the numbers under the square root.

$$5\sqrt{102}-151\sqrt{51}$$