Solve -2(sqrt{75}-sqrt{147})

$$- 2 ( \sqrt { 75 } - \sqrt { 147 } )$$

Evaluate

$$4\sqrt{3}\approx 6.92820323$$

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}.

$$-2\left(5\sqrt{3}-\sqrt{147}\right)$$

Factor 147=7^{2}\times 3. Rewrite the square root of the product \sqrt{7^{2}\times 3} as the product of square roots \sqrt{7^{2}}\sqrt{3}. Take the square root of 7^{2}.

$$-2\left(5\sqrt{3}-7\sqrt{3}\right)$$

Combine 5\sqrt{3} and -7\sqrt{3} to get -2\sqrt{3}.

$$-2\left(-2\right)\sqrt{3}$$

Multiply -2 and -2 to get 4.

$$4\sqrt{3}$$