Solve (sqrt{48}-sqrt{75})*sqrt{3}

$$( \sqrt { 48 } - \sqrt { 75 } ) \times \sqrt { 3 }$$

Evaluate

$$-3$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\left(4\sqrt{3}-\sqrt{75}\right)\sqrt{3}$$

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}.

$$\left(4\sqrt{3}-5\sqrt{3}\right)\sqrt{3}$$

Combine 4\sqrt{3} and -5\sqrt{3} to get -\sqrt{3}.

$$-\sqrt{3}\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$-3$$

Factor

$$-3$$