Solve 4sqrt{2}-2sqrt{8}+3/sqrt{2}

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

Evaluate

$$\frac{3\sqrt{2}}{2}\approx 2.121320344$$

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}.

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

Multiply -2 and 2 to get -4.

$$4\sqrt{2}-4\sqrt{2}+\frac{3}{\sqrt{2}}$$

Combine 4\sqrt{2} and -4\sqrt{2} to get 0.

$$\frac{3}{\sqrt{2}}$$

Rationalize the denominator of \frac{3}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{2}}{2}$$