Estimating Square Roots worksheet for math practice.

It looks like you've uploaded a worksheet titled "Estimating Square Roots", which asks students to estimate the square roots of various numbers and identify between which two consecutive whole numbers each square root lies.

Since I can't view images directly, I’ll help you solve this type of problem step by step based on typical content found in such worksheets. Let's assume the worksheet contains problems like:

---

Example Problems:

1. √10 is between ___ and ___
2. √25 is between ___ and ___
3. √47 is between ___ and ___
4. √80 is between ___ and ___
5. √100 is between ___ and ___

And so on...

---

Step-by-Step Guide to Estimating Square Roots:

To estimate a square root, follow these steps:

1. Find perfect squares near the number.
2. Determine which two consecutive whole numbers the square root lies between.
3. The square root will be between the square roots of those perfect squares.

---

Let’s Solve Some Examples:

#### 1. √10
- Perfect squares:
- √9 = 3
- √16 = 4
- Since 10 is between 9 and 16, √10 is between 3 and 4.

✔ Answer: 3 and 4

---

#### 2. √25
- √25 = 5 exactly
- So it's between 5 and 5? But since we want *consecutive* whole numbers, we say it's between 5 and 5, but usually, we just say it equals 5.

But if the question says "between two consecutive whole numbers", then since 25 is a perfect square, √25 = 5, so it lies between 5 and 5 — but that's not two different numbers.

Wait — actually, √25 = 5, so it is exactly 5, meaning it lies between 4 and 5? No! That would be wrong.

Let’s clarify:

- √25 = 5 → So it is equal to 5, not between 5 and 6.
- But if the question wants two consecutive integers between which the square root lies, then for √25, since it's exactly 5, it's not between two different integers — it is one of them.

So the correct answer is: 5 and 5 (but typically, we say √25 = 5).

However, most worksheets expect the format: “is between ___ and ___” even for perfect squares.

So:
- √25 = 5 → lies between 5 and 5 — or sometimes they accept “5 and 5” or just note it’s exact.

But more accurately, since 5² = 25, then √25 = 5 → so it is between 5 and 5.

But let's suppose the worksheet wants the two whole numbers such that:
> a < √x < b

Then for perfect squares, this doesn’t work unless we allow equality.

But often, the instruction says: “Between which two consecutive whole numbers does the square root lie?”

For √25:
- It is exactly 5, so it lies between 5 and 6? No — because 5 is less than 5? No.

Actually, the square root of 25 is exactly 5, so it does not lie between two consecutive whole numbers — it is equal to one.

But in many cases, the worksheet allows answers like:
- √25 is between 5 and 5 (if allowed)
- Or perhaps the problem skips perfect squares.

Let’s try another:

---

#### 3. √47
- Perfect squares:
- √36 = 6
- √49 = 7
- 47 is between 36 and 49 → √47 is between 6 and 7

✔ Answer: 6 and 7

---

#### 4. √80
- √64 = 8
- √81 = 9
- 80 is between 64 and 81 → √80 is between 8 and 9

✔ Answer: 8 and 9

---

#### 5. √100
- √100 = 10 → so it is exactly 10
- So √100 is between 10 and 10 — or just 10

But again, if asking for two consecutive whole numbers, technically it's not between two different ones.

But if we say: "Which two consecutive whole numbers is √100 between?" → answer is 10 and 11? No — because 10 < √100 = 10 → false.

So only valid way: √100 = 10 → lies between 9 and 10? No — 10 is not between 9 and 10.

So correct answer: 10 and 10

But most teachers accept: “between 10 and 10” or simply recognize it as a perfect square.

Alternatively, some versions of the worksheet may skip perfect squares.

---

General Strategy:

| Number | Closest Perfect Squares | Estimate |
|--------|--------------------------|---------|
| √10 | 9 and 16 → 3 and 4 | Between 3 and 4 |
| √15 | 9 and 16 → 3 and 4 | Between 3 and 4 |
| √20 | 16 and 25 → 4 and 5 | Between 4 and 5 |
| √30 | 25 and 36 → 5 and 6 | Between 5 and 6 |
| √50 | 49 and 64 → 7 and 8 | Between 7 and 8 |
| √75 | 64 and 81 → 8 and 9 | Between 8 and 9 |

---

Final Tips:

- Know your perfect squares:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, ...
- For any number x, find the perfect squares around it.
- Then take their square roots.

---

Example Worksheet Answers (Assumed):

| Problem | Answer |
|--------|--------|
| √10 is between | 3 and 4 |
| √15 is between | 3 and 4 |
| √25 is between | 5 and 5 (or just 5) |
| √30 is between | 5 and 6 |
| √47 is between | 6 and 7 |
| √50 is between | 7 and 8 |
| √75 is between | 8 and 9 |
| √80 is between | 8 and 9 |
| √99 is between | 9 and 10 |
| √100 is between | 10 and 10 |

---

If you can provide the exact numbers from your worksheet (e.g., list of square roots), I can give you the precise answers.

Otherwise, use the method above to fill in the blanks.

Would you like me to generate a completed version of this worksheet with answers based on common problems?