Solve frac{3sqrt{10}}{sqrt{8}}

$$\frac{ 3 \sqrt{ 10 } }{ \sqrt{ 8 } }$$

Evaluate

$$\frac{3\sqrt{5}}{2}\approx 3.354101966$$

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}.

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

Rationalize the denominator of \frac{3\sqrt{10}}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{10}\sqrt{2}}{2\times 2}$$

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

$$\frac{3\sqrt{2}\sqrt{5}\sqrt{2}}{2\times 2}$$

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

$$\frac{3\times 2\sqrt{5}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{3\times 2\sqrt{5}}{4}$$

Multiply 3 and 2 to get 6.

$$\frac{6\sqrt{5}}{4}$$

Divide 6\sqrt{5} by 4 to get \frac{3}{2}\sqrt{5}.

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