Solve (46+20+17+64)/sqrt{22780}

$$\frac{ (46+20+17+64) }{ \sqrt{ 22780 } }$$

Evaluate

$$\frac{147\sqrt{5695}}{11390}\approx 0.973958551$$

Solution Steps

Add 46 and 20 to get 66.

$$\frac{66+17+64}{\sqrt{22780}}$$

Add 66 and 17 to get 83.

$$\frac{83+64}{\sqrt{22780}}$$

Add 83 and 64 to get 147.

$$\frac{147}{\sqrt{22780}}$$

Factor 22780=2^{2}\times 5695. Rewrite the square root of the product \sqrt{2^{2}\times 5695} as the product of square roots \sqrt{2^{2}}\sqrt{5695}. Take the square root of 2^{2}.

$$\frac{147}{2\sqrt{5695}}$$

Rationalize the denominator of \frac{147}{2\sqrt{5695}} by multiplying numerator and denominator by \sqrt{5695}.

$$\frac{147\sqrt{5695}}{2\left(\sqrt{5695}\right)^{2}}$$

The square of \sqrt{5695} is 5695.

$$\frac{147\sqrt{5695}}{2\times 5695}$$

Multiply 2 and 5695 to get 11390.

$$\frac{147\sqrt{5695}}{11390}$$