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Answer
The negative square root of 4 is -2.
Solution
The negative square root of 4 is **-2**.
Here's why:
- **Square Root Definition:** The square root of a number \( x \) is a value that, when multiplied by itself, gives \( x \).
- **For 4:**
\[
\sqrt{4} = 2 \quad \text{because} \quad 2 \times 2 = 4
\]
- **Negative Square Root:**
\[
-\sqrt{4} = -2 \quad \text{because} \quad (-2) \times (-2) = 4
\]
So, while the principal (or positive) square root of 4 is **2**, the **negative** square root is **-2**.
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Simplify this solution The Deep Dive
The negative square root of 4 is -2. When we talk about square roots, we're usually looking for both the positive and negative solutions to the equation. In this case, since 2 multiplied by itself equals 4, then -2 is also a valid solution because -2 times -2 is also 4! If you ever find yourself puzzled by square roots, remember that every positive number has two square roots: one positive and one negative. So, don’t just stop at the positive—always be on the lookout for the negative as well!
