Solve 147/sqrt{35380}

$$\frac{ 147 }{ \sqrt{ 35380 } }$$

Evaluate

$$\frac{147\sqrt{8845}}{17690}\approx 0.781516984$$

Solution Steps

Factor 35380=2^{2}\times 8845. Rewrite the square root of the product \sqrt{2^{2}\times 8845} as the product of square roots \sqrt{2^{2}}\sqrt{8845}. Take the square root of 2^{2}.

$$\frac{147}{2\sqrt{8845}}$$

Rationalize the denominator of \frac{147}{2\sqrt{8845}} by multiplying numerator and denominator by \sqrt{8845}.

$$\frac{147\sqrt{8845}}{2\left(\sqrt{8845}\right)^{2}}$$

The square of \sqrt{8845} is 8845.

$$\frac{147\sqrt{8845}}{2\times 8845}$$

Multiply 2 and 8845 to get 17690.

$$\frac{147\sqrt{8845}}{17690}$$