Question

simplify.
\frac{\sqrt{115}}{\sqrt{5}}
suggested tutorial:
learn it: multiply radical expressions.
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Explanation:

Step1: Simplify the fraction inside the radical

First, we simplify the fraction \(\frac{115}{5}\). Since \(115\div5 = 23\), we have \(\frac{115}{5}=23\).

Step2: Take the square root

Now we need to find the square root of \(23\), but since \(23\) is a prime number, \(\sqrt{23}\) cannot be simplified further. Wait, no, wait. Wait, the original expression is \(\frac{\sqrt{115}}{\sqrt{5}}\). Using the property of radicals \(\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}\) (for \(a\geq0\) and \(b > 0\)), so \(\frac{\sqrt{115}}{\sqrt{5}}=\sqrt{\frac{115}{5}}\). Then, as we calculated, \(\frac{115}{5} = 23\), so \(\sqrt{\frac{115}{5}}=\sqrt{23}\). Wait, but maybe I misread the problem. Wait, the problem is to simplify \(\frac{\sqrt{115}}{\sqrt{5}}\). Using the quotient rule for radicals: \(\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}\), so \(\frac{\sqrt{115}}{\sqrt{5}}=\sqrt{\frac{115}{5}}=\sqrt{23}\). Wait, but let's check the calculation of \(\frac{115}{5}\). \(5\times23 = 115\), so \(\frac{115}{5}=23\). So then \(\sqrt{23}\) is the simplified form? Wait, no, maybe the problem was written as \(\frac{\sqrt{115}}{\sqrt{5}}\), and we can rationalize or simplify. Wait, \(\frac{\sqrt{115}}{\sqrt{5}}=\frac{\sqrt{5\times23}}{\sqrt{5}}=\frac{\sqrt{5}\times\sqrt{23}}{\sqrt{5}}=\sqrt{23}\). Yes, that's correct. So the simplified form is \(\sqrt{23}\).

Answer:

\(\sqrt{23}\)