Solve 15/sqrt{25+25}

$$\frac{ 15 }{ \sqrt{ 25+25 } }$$

Evaluate

$$\frac{3\sqrt{2}}{2}\approx 2.121320344$$

Solution Steps

Add 25 and 25 to get 50.

$$\frac{15}{\sqrt{50}}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$\frac{15}{5\sqrt{2}}$$

Rationalize the denominator of \frac{15}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{15\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{15\sqrt{2}}{5\times 2}$$

Cancel out 5 in both numerator and denominator.

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