Question
Simplify the following (write your answer as a fraction or a decimal). \[ (0,25)^{\frac{1}{2}} \]
Ask by Park Love. in South Africa
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified answer is \( \frac{1}{2} \).
Solution
1. Recognize that \( 0,25 \) is equivalent to \( 0.25 \) in decimal notation.
2. Express \( 0.25 \) as a fraction:
\[
0.25 = \frac{25}{100} = \frac{1}{4}
\]
3. Compute the square root:
\[
\left(\frac{1}{4}\right)^{\frac{1}{2}} = \sqrt{\frac{1}{4}} = \frac{\sqrt{1}}{\sqrt{4}} = \frac{1}{2}
\]
Final answer: \( \frac{1}{2} \)
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Simplify this solution Extra Insights
The expression \( (0.25)^{\frac{1}{2}} \) represents the square root of 0.25. To simplify it, we can rewrite 0.25 as a fraction: \( 0.25 = \frac{25}{100} = \frac{1}{4} \). Now, taking the square root: \[ (0.25)^{\frac{1}{2}} = \left(\frac{1}{4}\right)^{\frac{1}{2}} = \frac{1^{\frac{1}{2}}}{4^{\frac{1}{2}}} = \frac{1}{2} \] Thus, the simplified form is \( \frac{1}{2} \) or \( 0.5 \).
