Solve 3sqrt{2}+sqrt{5}divsqrt{2}+1

$$3 \sqrt{ 2 } + \sqrt{ 5 } \div \sqrt{ 2 } +1$$

Evaluate

$$\frac{\sqrt{10}}{2}+3\sqrt{2}+1\approx 6.823779517$$

Short Solution Steps

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$3\sqrt{2}+\frac{\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+1$$

The square of \sqrt{2} is 2.

$$3\sqrt{2}+\frac{\sqrt{5}\sqrt{2}}{2}+1$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$3\sqrt{2}+\frac{\sqrt{10}}{2}+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3\sqrt{2}+1 times \frac{2}{2}.

$$\frac{2\left(3\sqrt{2}+1\right)}{2}+\frac{\sqrt{10}}{2}$$

Since \frac{2\left(3\sqrt{2}+1\right)}{2} and \frac{\sqrt{10}}{2} have the same denominator, add them by adding their numerators.

$$\frac{2\left(3\sqrt{2}+1\right)+\sqrt{10}}{2}$$

Do the multiplications in 2\left(3\sqrt{2}+1\right)+\sqrt{10}.

$$\frac{6\sqrt{2}+2+\sqrt{10}}{2}$$