Question
Simplify the radical expression. \( \sqrt{28} \)
Ask by Ellis Luna. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \sqrt{28} = 2\sqrt{7} \)
Solution
To simplify the radical expression \( \sqrt{28} \), follow these steps:
1. **Factor the Number Inside the Radical:**
Start by finding the prime factors of 28.
\[
28 = 4 \times 7
\]
Here, 4 is a perfect square since \( 4 = 2^2 \).
2. **Apply the Square Root to Each Factor:**
Use the property of square roots that \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \).
\[
\sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7}
\]
3. **Simplify the Square Roots:**
Since \( \sqrt{4} = 2 \), substitute this value back into the expression.
\[
\sqrt{4} \times \sqrt{7} = 2 \times \sqrt{7}
\]
4. **Final Simplified Form:**
\[
\sqrt{28} = 2\sqrt{7}
\]
**Therefore, the simplified form of \( \sqrt{28} \) is \( 2\sqrt{7} \).**
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Simplify this solution Bonus Knowledge
To simplify \( \sqrt{28} \), we start by finding the prime factorization of 28. It can be broken down as \( 28 = 4 \times 7 \), where 4 is a perfect square. So, we can express the square root as follows: \[ \sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7} = 2\sqrt{7}. \] Thus, the simplified form of \( \sqrt{28} \) is \( 2\sqrt{7} \). Now, isn’t it neat how we can break down numbers and uncover their simpler forms? Next time you encounter a radical, just remember you can factor it to make your life easier!
