Solve 4-sqrt{8}+1+sqrt{18}

$$4- \sqrt{ 8 } +1+ \sqrt{ 18 }$$

Evaluate

$$\sqrt{2}+5\approx 6.414213562$$

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}.

$$4-2\sqrt{2}+1+\sqrt{18}$$

Add 4 and 1 to get 5.

$$5-2\sqrt{2}+\sqrt{18}$$

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}.

$$5-2\sqrt{2}+3\sqrt{2}$$

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

$$5+\sqrt{2}$$