Solve 3sqrt{8}*(sqrt{54}-5sqrt{2}-2sqrt{6})

$$3 \sqrt { 8 } \times ( \sqrt { 54 } - 5 \sqrt { 2 } - 2 \sqrt { 6 } )$$

Evaluate

$$12\left(\sqrt{3}-5\right)\approx -39.215390309$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$3\times 2\sqrt{2}\left(\sqrt{54}-5\sqrt{2}-2\sqrt{6}\right)$$

Multiply 3 and 2 to get 6.

$$6\sqrt{2}\left(\sqrt{54}-5\sqrt{2}-2\sqrt{6}\right)$$

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

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

Combine 3\sqrt{6} and -2\sqrt{6} to get \sqrt{6}.

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

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

$$6\sqrt{2}\sqrt{6}-30\left(\sqrt{2}\right)^{2}$$

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}.

$$6\sqrt{2}\sqrt{2}\sqrt{3}-30\left(\sqrt{2}\right)^{2}$$

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

$$6\times 2\sqrt{3}-30\left(\sqrt{2}\right)^{2}$$

Multiply 6 and 2 to get 12.

$$12\sqrt{3}-30\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$12\sqrt{3}-30\times 2$$

Multiply -30 and 2 to get -60.

$$12\sqrt{3}-60$$