Solve (sqrt{48}-sqrt{50}+sqrt{75})(-sqrt{6})

$$( \sqrt { 48 } - \sqrt { 50 } + \sqrt { 75 } ) ( - \sqrt { 6 } )$$

Evaluate

$$10\sqrt{3}-27\sqrt{2}\approx -20.863258108$$

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}.

$$\left(4\sqrt{3}-\sqrt{50}+\sqrt{75}\right)\left(-\sqrt{6}\right)$$

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}.

$$\left(4\sqrt{3}-5\sqrt{2}+\sqrt{75}\right)\left(-\sqrt{6}\right)$$

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}.

$$\left(4\sqrt{3}-5\sqrt{2}+5\sqrt{3}\right)\left(-\sqrt{6}\right)$$

Combine 4\sqrt{3} and 5\sqrt{3} to get 9\sqrt{3}.

$$\left(9\sqrt{3}-5\sqrt{2}\right)\left(-\sqrt{6}\right)$$

Use the distributive property to multiply 9\sqrt{3}-5\sqrt{2} by -\sqrt{6}.

$$9\sqrt{3}\left(-\sqrt{6}\right)-5\sqrt{2}\left(-\sqrt{6}\right)$$

Multiply -5 and -1 to get 5.

$$9\sqrt{3}\left(-\sqrt{6}\right)+5\sqrt{2}\sqrt{6}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$9\sqrt{3}\left(-\sqrt{6}\right)+5\sqrt{2}\sqrt{2}\sqrt{3}$$

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

$$9\sqrt{3}\left(-\sqrt{6}\right)+5\times 2\sqrt{3}$$

Multiply 5 and 2 to get 10.

$$9\sqrt{3}\left(-\sqrt{6}\right)+10\sqrt{3}$$

Multiply 9 and -1 to get -9.

$$-9\sqrt{3}\sqrt{6}+10\sqrt{3}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$-9\sqrt{3}\sqrt{3}\sqrt{2}+10\sqrt{3}$$

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

$$-9\times 3\sqrt{2}+10\sqrt{3}$$

Multiply -9 and 3 to get -27.

$$-27\sqrt{2}+10\sqrt{3}$$