Solve sqrt{45div8}

$$\sqrt{ 45 \div 8 }$$

Evaluate

$$\frac{3\sqrt{10}}{4}\approx 2.371708245$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{45}{8}} as the division of square roots \frac{\sqrt{45}}{\sqrt{8}}.

$$\frac{\sqrt{45}}{\sqrt{8}}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$\frac{3\sqrt{5}}{\sqrt{8}}$$

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}.

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

Rationalize the denominator of \frac{3\sqrt{5}}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

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

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

Multiply 2 and 2 to get 4.

$$\frac{3\sqrt{10}}{4}$$