Solve 500/sqrt{220sqrt{1150}}

$$\frac{ 500 }{ \sqrt{ 220 } \sqrt{ 1150 } }$$

Evaluate

$$\frac{5\sqrt{2530}}{253}\approx 0.994053466$$

Solution Steps

Factor 220=2^{2}\times 55. Rewrite the square root of the product \sqrt{2^{2}\times 55} as the product of square roots \sqrt{2^{2}}\sqrt{55}. Take the square root of 2^{2}.

$$\frac{500}{2\sqrt{55}\sqrt{1150}}$$

Factor 1150=5^{2}\times 46. Rewrite the square root of the product \sqrt{5^{2}\times 46} as the product of square roots \sqrt{5^{2}}\sqrt{46}. Take the square root of 5^{2}.

$$\frac{500}{2\sqrt{55}\times 5\sqrt{46}}$$

Multiply 2 and 5 to get 10.

$$\frac{500}{10\sqrt{55}\sqrt{46}}$$

To multiply \sqrt{55} and \sqrt{46}, multiply the numbers under the square root.

$$\frac{500}{10\sqrt{2530}}$$

Rationalize the denominator of \frac{500}{10\sqrt{2530}} by multiplying numerator and denominator by \sqrt{2530}.

$$\frac{500\sqrt{2530}}{10\left(\sqrt{2530}\right)^{2}}$$

The square of \sqrt{2530} is 2530.

$$\frac{500\sqrt{2530}}{10\times 2530}$$

Cancel out 10\times 10 in both numerator and denominator.

$$\frac{5\sqrt{2530}}{253}$$