Solve (sqrt{16}+sqrt{24})(1-sqrt{6})

$$( \sqrt { 16 } + \sqrt { 24 } ) ( 1 - \sqrt { 6 } )$$

Evaluate

$$-2\sqrt{6}-8\approx -12.898979486$$

Solution Steps

Calculate the square root of 16 and get 4.

$$\left(4+\sqrt{24}\right)\left(1-\sqrt{6}\right)$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\left(4+2\sqrt{6}\right)\left(1-\sqrt{6}\right)$$

Apply the distributive property by multiplying each term of 4+2\sqrt{6} by each term of 1-\sqrt{6}.

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

Combine -4\sqrt{6} and 2\sqrt{6} to get -2\sqrt{6}.

$$4-2\sqrt{6}-2\left(\sqrt{6}\right)^{2}$$

The square of \sqrt{6} is 6.

$$4-2\sqrt{6}-2\times 6$$

Multiply -2 and 6 to get -12.

$$4-2\sqrt{6}-12$$

Subtract 12 from 4 to get -8.

$$-8-2\sqrt{6}$$