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Certainly! Let's solve the expression step-by-step.
Given the expression: [tex]\[ \sqrt{\frac{1}{a} + \frac{1}{a}} \][/tex]
1. Simplify the expression inside the square root: We start by combining the terms inside the square root. [tex]\[ \frac{1}{a} + \frac{1}{a} \][/tex] Since these are like terms, we can add them together: [tex]\[ \frac{1}{a} + \frac{1}{a} = \frac{1}{a} \cdot 2 = \frac{2}{a} \][/tex]
2. Take the square root of the simplified expression: Now our expression becomes the square root of [tex]\(\frac{2}{a}\)[/tex]: [tex]\[ \sqrt{\frac{2}{a}} \][/tex]
3. Simplify the square root: We can rewrite the square root of a quotient as the quotient of the square roots: [tex]\[ \sqrt{\frac{2}{a}} = \frac{\sqrt{2}}{\sqrt{a}} \][/tex]
4. Combine the radicals: To make it look neater, we can combine the radicals if needed, but in this case, [tex]\(\sqrt{2}\)[/tex] and [tex]\(\sqrt{a}\)[/tex] are already in their simplest forms.
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