Solve sqrt{150}-sqrt{75}*2sqrt{50}

$$\sqrt { 150 } - \sqrt { 75 } \times 2 \sqrt { 50 }$$

Evaluate

$$-45\sqrt{6}\approx -110.227038425$$

Solution Steps

Factor 150=5^{2}\times 6. Rewrite the square root of the product \sqrt{5^{2}\times 6} as the product of square roots \sqrt{5^{2}}\sqrt{6}. Take the square root of 5^{2}.

$$5\sqrt{6}-2\sqrt{75}\sqrt{50}$$

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}.

$$5\sqrt{6}-2\times 5\sqrt{3}\sqrt{50}$$

Multiply 2 and 5 to get 10.

$$5\sqrt{6}-10\sqrt{3}\sqrt{50}$$

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}.

$$5\sqrt{6}-10\sqrt{3}\times 5\sqrt{2}$$

Multiply 10 and 5 to get 50.

$$5\sqrt{6}-50\sqrt{3}\sqrt{2}$$

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

$$5\sqrt{6}-50\sqrt{6}$$

Combine 5\sqrt{6} and -50\sqrt{6} to get -45\sqrt{6}.

$$-45\sqrt{6}$$