We're glad you stopped by Your friend finds tex pm sqrt frac 1 25 tex Is your friend correct Explain your reasoning tex pm sqrt frac 1 25 pm frac. This page is here to walk you through essential details with clear and straightforward explanations. Our goal is to make your learning experience easy, enriching, and enjoyable. Start exploring and find the information you need!
Answer :
Sure, let's go through the question step by step.
Question:
>Your friend finds [tex]\( \pm \sqrt{\frac{1}{25}} \)[/tex]. Is your friend correct? Explain your reasoning.
>
>[tex]\( \pm \sqrt{\frac{1}{25}} = \pm \frac{1}{5} \)[/tex]
Solution:
1. Understanding the expression:
- The problem involves the square root of the fraction [tex]\(\frac{1}{25}\)[/tex].
2. Evaluating the square root:
- When you take the square root of a fraction, you take the square root of the numerator and the square root of the denominator separately.
- So, [tex]\( \sqrt{\frac{1}{25}} = \sqrt{1} / \sqrt{25} \)[/tex].
3. Calculating the square roots:
- [tex]\( \sqrt{1} \)[/tex] is 1.
- [tex]\( \sqrt{25} \)[/tex] is 5.
4. Putting it all together:
- Therefore, [tex]\( \sqrt{\frac{1}{25}} = \frac{\sqrt{1}}{\sqrt{25}} = \frac{1}{5} \)[/tex].
5. Including the positive and negative signs:
- Since we are dealing with square roots, there are two possible values, a positive and a negative value. Thus, [tex]\( \pm \sqrt{\frac{1}{25}} = \pm \frac{1}{5} \)[/tex].
6. Conclusion:
- Yes, your friend is correct. The expression [tex]\( \pm \sqrt{\frac{1}{25}} \)[/tex] indeed equals [tex]\( \pm \frac{1}{5} \)[/tex].
By following these steps clearly, we understand that the initial evaluation and conclusion your friend made are accurate. [tex]\( \pm \sqrt{\frac{1}{25}} \)[/tex] is indeed [tex]\( \pm \frac{1}{5} \)[/tex].
Question:
>Your friend finds [tex]\( \pm \sqrt{\frac{1}{25}} \)[/tex]. Is your friend correct? Explain your reasoning.
>
>[tex]\( \pm \sqrt{\frac{1}{25}} = \pm \frac{1}{5} \)[/tex]
Solution:
1. Understanding the expression:
- The problem involves the square root of the fraction [tex]\(\frac{1}{25}\)[/tex].
2. Evaluating the square root:
- When you take the square root of a fraction, you take the square root of the numerator and the square root of the denominator separately.
- So, [tex]\( \sqrt{\frac{1}{25}} = \sqrt{1} / \sqrt{25} \)[/tex].
3. Calculating the square roots:
- [tex]\( \sqrt{1} \)[/tex] is 1.
- [tex]\( \sqrt{25} \)[/tex] is 5.
4. Putting it all together:
- Therefore, [tex]\( \sqrt{\frac{1}{25}} = \frac{\sqrt{1}}{\sqrt{25}} = \frac{1}{5} \)[/tex].
5. Including the positive and negative signs:
- Since we are dealing with square roots, there are two possible values, a positive and a negative value. Thus, [tex]\( \pm \sqrt{\frac{1}{25}} = \pm \frac{1}{5} \)[/tex].
6. Conclusion:
- Yes, your friend is correct. The expression [tex]\( \pm \sqrt{\frac{1}{25}} \)[/tex] indeed equals [tex]\( \pm \frac{1}{5} \)[/tex].
By following these steps clearly, we understand that the initial evaluation and conclusion your friend made are accurate. [tex]\( \pm \sqrt{\frac{1}{25}} \)[/tex] is indeed [tex]\( \pm \frac{1}{5} \)[/tex].
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