Solve (6sqrt{8}+8sqrt{18}-4sqrt{50})div2sqrt{2}=

$$( 6 \sqrt { 8 } + 8 \sqrt { 18 } - 4 \sqrt { 50 } ) \div 2 \sqrt { 2 } =$$

Evaluate

$$16$$

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}.

$$\frac{6\times 2\sqrt{2}+8\sqrt{18}-4\sqrt{50}}{2}\sqrt{2}$$

Multiply 6 and 2 to get 12.

$$\frac{12\sqrt{2}+8\sqrt{18}-4\sqrt{50}}{2}\sqrt{2}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{12\sqrt{2}+8\times 3\sqrt{2}-4\sqrt{50}}{2}\sqrt{2}$$

Multiply 8 and 3 to get 24.

$$\frac{12\sqrt{2}+24\sqrt{2}-4\sqrt{50}}{2}\sqrt{2}$$

Combine 12\sqrt{2} and 24\sqrt{2} to get 36\sqrt{2}.

$$\frac{36\sqrt{2}-4\sqrt{50}}{2}\sqrt{2}$$

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}.

$$\frac{36\sqrt{2}-4\times 5\sqrt{2}}{2}\sqrt{2}$$

Multiply -4 and 5 to get -20.

$$\frac{36\sqrt{2}-20\sqrt{2}}{2}\sqrt{2}$$

Combine 36\sqrt{2} and -20\sqrt{2} to get 16\sqrt{2}.

$$\frac{16\sqrt{2}}{2}\sqrt{2}$$

Divide 16\sqrt{2} by 2 to get 8\sqrt{2}.

$$8\sqrt{2}\sqrt{2}$$

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

$$8\times 2$$

Multiply 8 and 2 to get 16.

$$16$$

Factor

$$2^{4}$$