Square Root Worksheets - Free Printable

Let's solve each part of the problem step by step.

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Part A: Find the values of the following square roots

We are to find the square root of perfect squares.

#### a) √4841

Let’s check if 4841 is a perfect square. Try squaring numbers around √4841:

- 69² = 4761
- 70² = 4900

So, 4841 is between 69² and 70². But it's not a perfect square. Wait — let's double-check.

Wait! Let's test:
- 69² = 4761
- 70² = 4900 → So 4841 is not a perfect square.

But wait — maybe we made an error? Let's try 69.5²?

Actually, perhaps this is a typo or trick question.

Wait — let’s check 69² = 4761, 70² = 4900, so no integer square root for 4841. But the problem says "perfect square", so likely a mistake?

Wait — look again: maybe it's 484, not 4841?

But as written: √4841 — that's not a perfect square.

Wait — let’s try 69.5² = ?
69.5² = (70 - 0.5)² = 4900 - 70 + 0.25 = 4830.25

Still less than 4841.

Try 69.6² = ?

But let’s skip and come back.

Wait — perhaps it’s √484, which is 22² = 484 → √484 = 22

But here it's 4841, which is not a perfect square.

Wait — maybe it's a typo? Or perhaps it's √484?

But the number is clearly 4841.

Let me check: Is there any number whose square is 4841?

Try 69.5² = 4830.25
69.6² = (69.5 + 0.1)² = 69.5² + 2×69.5×0.1 + 0.01 = 4830.25 + 13.9 + 0.01 = 4844.16 → too high

69.5² = 4830.25
69.55² = ?

Alternatively, let’s just accept that 4841 is not a perfect square, but the problem says “Perfect Square” — so maybe it's a typo?

Wait — perhaps it's √484, and the image has a typo?

But let's move on and see others.

#### b) √1625

Check if 1625 is a perfect square.

- 40² = 1600
- 41² = 1681 → so between them. Not a perfect square.

#### c) √736

- 27² = 729
- 28² = 784 → 736 is in between → not a perfect square

#### d) √1924

- 43² = 1849
- 44² = 1936 → 1924 < 1936 → not a perfect square

#### e) √4000

- 63² = 3969
- 64² = 4096 → not a perfect square

#### f) √800

- 28² = 784
- 29² = 841 → not a perfect square

Hmm — none of these seem to be perfect squares?

Wait — maybe I misread.

Wait — let's go back.

Perhaps the numbers are not all perfect squares, but the problem says "Perfect Square" — maybe it's a title?

Wait — the heading says: Square Root – Perfect Square

So probably, all these are perfect squares — so maybe I made a mistake.

Let’s recheck:

a) √4841 — is this a perfect square?

Try 69² = 4761
70² = 4900
69.5² = 4830.25
69.6² = 69.5² + 2×69.5×0.1 + 0.01 = 4830.25 + 13.9 + 0.01 = 4844.16 → too big

So 69.5² = 4830.25
69.55² = ?

Not helpful.

Wait — maybe it's √484? Then answer is 22.

But the number is written as 4841 — perhaps it's a typo.

Wait — let’s look at g): √144 — that’s easy: 12² = 144 → √144 = 12

h) √841 — 29² = 841 → √841 = 29

i) √2401 — 49² = 2401 → √2401 = 49

j) √825 — 28² = 784, 29² = 841 → not a perfect square

k) √8100 — 90² = 8100 → √8100 = 90

l) √3.61 — 1.9² = 3.61 → √3.61 = 1.9

Now, going back — only some of them are perfect squares.

But the problem says "Perfect Square", so likely only those that are perfect squares are intended.

Wait — perhaps the first few are not perfect squares, but the later ones are?

Let’s list all:

a) √4841 — not a perfect square
b) √1625 — not
c) √736 — not
d) √1924 — not
e) √4000 — not
f) √800 — not
g) √144 — yes → 12
h) √841 — yes → 29
i) √2401 — yes → 49
j) √825 — not
k) √8100 — yes → 90
l) √3.61 — yes → 1.9

So maybe the first six are meant to be approximated, but the problem says “Perfect Square”, so likely only g, h, i, k, l are perfect squares.

But the instruction says “Find the value of the following” — so perhaps we need to compute exact values.

But if they are not perfect squares, then we can’t write exact integers.

Wait — perhaps I miscalculated.

Let’s try √4841 again.

Is 69.5² = 4830.25
69.6² = 4844.16 — too big
So √4841 ≈ 69.57 — not integer.

But maybe the number is 484, not 4841? That would make sense.

Similarly, 1625: 40.3² ≈ 1624.09 — close, but not exact.

Wait — let’s look at Part B:

> Find the square roots of the following numerals.
> g) 144 → 12
> h) 841 → 29
> i) 2401 → 49
> j) 825 → not perfect square
> k) 8100 → 90
> l) 3.61 → 1.9

So likely, the first six in Part A are not perfect squares — but the problem might have a typo, or perhaps it's asking for approximate values?

But the heading says "Perfect Square", so probably only perfect squares are included.

Wait — perhaps Part A is about perfect squares, so only those that are perfect squares should be solved.

But the way it's listed, it's numbered a through l.

Alternatively, maybe Part A is just listing square roots to evaluate, not necessarily perfect squares.

But the title says "Perfect Square".

Let’s assume that only perfect squares are to be evaluated exactly.

So let’s focus on:

Part B: Find the square roots of the following numerals

These are:

g) 144 → √144 = 12
h) 841 → √841 = 29
i) 2401 → √2401 = 49
j) 825 → not a perfect square → √825 ≈ 28.72
k) 8100 → √8100 = 90
l) 3.61 → √3.61 = 1.9

But 825 is not a perfect square.

Wait — 825 = 25 × 33 → √825 = √(25×33) = 5√33 ≈ 5×5.744 = 28.72

But maybe it's a typo — perhaps 841?

No, 841 is already listed.

Wait — maybe j) is √825 — but not a perfect square.

But let’s check k) √8100 — 90² = 8100 → yes

l) √3.61 — 1.9² = 3.61 → yes

So only g, h, i, k, l are perfect squares.

But j) 825 — not perfect square.

Wait — perhaps it's 829? No.

Or 841? Already used.

Wait — maybe j) is 825, and we leave it as irrational.

But the problem says “find the square roots” — so perhaps we need to simplify or approximate.

But since it's labeled “Perfect Square”, maybe only perfect squares are intended.

Alternatively, perhaps the numbers in Part A are supposed to be perfect squares.

Let me double-check:

Wait — maybe a) √4841 — is it possible?

Try 69.5² = 4830.25
69.6² = 4844.16 → too big

So no.

Wait — what about √484? That's 22.

Maybe it's 484, not 4841.

Similarly, b) √1625 — 40.3² = 1624.09 → close to 1625 — but not exact.

Wait — √1625 = √(25×65) = 5√65 — not rational.

But c) √736 — 27² = 729, 28² = 784 → not perfect square.

Wait — perhaps d) √1924 — 43² = 1849, 44² = 1936 → 1924 is not a perfect square.

But 43.8² = ? 43.8² = (44 - 0.2)² = 1936 - 2×44×0.2 + 0.04 = 1936 - 17.6 + 0.04 = 1918.44
43.9² = 1918.44 + 2×43.8×0.1 + 0.01 ≈ 1918.44 + 8.76 + 0.01 = 1927.21 → too big

So √1924 ≈ 43.86 — not integer.

So none of a-f are perfect squares.

But g) 144 — yes, 12
h) 841 — 29
i) 2401 — 49
k) 8100 — 90
l) 3.61 — 1.9

And j) 825 — not perfect square.

But wait — 825 = 25×33 → √825 = 5√33

But perhaps it's a typo and it's 841 or 8100?

Wait — 8100 is already listed.

Wait — maybe j) is 841? But h is already 841.

No.

Alternatively, perhaps j) is 825, and we're to leave it as √825 = 5√33

But the problem says “find the square roots” — so maybe approximate?

But let’s look at Part C:

> Which of the following is the square root of 8464?

Options:
a) 8.8
b) 9.2
c) 9.6
d) 9.8
e) 9.9

But 9.2² = 84.64
9.2² = (9 + 0.2)² = 81 + 3.6 + 0.04 = 84.64

But 8464 is much bigger.

Try 92² = ?

90² = 8100
92² = (90+2)² = 8100 + 360 + 4 = 8464 → YES!

So √8464 = 92

But options are decimals like 8.8, 9.2, etc.

9.2² = 84.64 — not 8464

So none of the options match 92.

But 92 is not among a-e.

Wait — perhaps the options are wrong?

Or perhaps it's a typo.

Wait — maybe the question is: “Which of the following is the square root of 84.64?”

Then 9.2² = 84.64 → so answer is b) 9.2

That makes sense.

Likely, the number is 84.64, not 8464.

Because 8464 is 92², but options are around 9.

So probably a typo in the question.

So C) asks: Which is the square root of 84.64?

Then:
- 9.2² = 84.64 → so answer is b) 9.2

Now, back to Part B:

g) √144 = 12
h) √841 = 29
i) √2401 = 49
j) √825 — not a perfect square → √825 = √(25×33) = 5√33 ≈ 28.72
k) √8100 = 90
l) √3.61 = 1.9

But the problem says “Perfect Square”, so maybe only perfect squares are expected.

But j) 825 is not a perfect square.

Wait — is 825 a perfect square? No.

But perhaps it's 841? Already used.

Wait — maybe it's 8100, but that's k.

Alternatively, perhaps j) is 841, but h is already 841.

No.

Wait — maybe j) is 825, and we are to approximate.

But let’s look at Part A — perhaps it's the same as Part B?

Wait — the image shows:

> Part A: Find the values of the following
> a) √4841
> b) √1625
> ...
> l) √3.61

Then Part B: Find the square roots of the following numerals
> g) 144
> h) 841
> ...
> l) 3.61

Wait — that’s strange — both parts have items labeled a-l, but Part B starts from g.

Possibly, Part A is a list of square roots to evaluate (some may not be perfect squares), and Part B is a separate list.

But the title says "Perfect Square", so maybe only perfect squares are to be considered.

But let’s assume that Part A includes non-perfect squares, and we need to find their approximate values.

But without a calculator, it’s hard.

Alternatively, perhaps the numbers are perfect squares, and I made a mistake.

Let’s check:

- √4841 — is it 69.5² = 4830.25, 69.6² = 4844.16 — so no.
- √1625 — 40.3² = 1624.09, 40.31² = 1624.09 + 2×40.3×0.01 + 0.0001 ≈ 1624.09 + 0.806 + 0.0001 = 1624.8961, still less than 1625
- 40.32² = 1624.8961 + 2×40.31×0.01 ≈ 1624.8961 + 0.8102 = 1625.7063 → too big

So √1625 ≈ 40.31

But not nice.

Wait — maybe a) is √484 = 22
b) √1625 — not nice
c) √736 — 27.13² ≈ 736? 27² = 729, 27.1² = 734.41, 27.2² = 739.84 → so √736 ≈ 27.13

But not exact.

But let’s go to Part C — it’s clearer.

Part C: Which of the following is the square root of 84.64?

Options:
a) 8.8
b) 9.2
c) 9.6
d) 9.8
e) 9.9

Compute:

- 8.8² = 77.44
- 9.2² = (9 + 0.2)² = 81 + 3.6 + 0.04 = 84.64 → YES!

So b) 9.2 is correct.

Answer: b) 9.2

Now, back to Part B:

g) √144 = 12
h) √841 = 29
i) √2401 = 49
j) √825 — not perfect square → but perhaps simplify: √825 = √(25×33) = 5√33
k) √8100 = 90
l) √3.61 = 1.9

So for Part B, answers are:

g) 12
h) 29
i) 49
j) 5√33 or approximately 28.72
k) 90
l) 1.9

But if only perfect squares, then j is skipped.

But the problem says "find the square roots", so we include all.

Now, Part A seems to be the same as Part B, but with different numbers.

Wait — looking at the image, Part A has a) to l), and Part B has g) to l) — overlapping.

Possibly, Part A is a list of square roots to evaluate, and Part B is another list.

But let’s assume the following:

Final Answers:

#### Part A:
a) √4841 — not a perfect square → approximately 69.57
b) √1625 — not perfect square → approximately 40.31
c) √736 — not perfect square → approximately 27.13
d) √1924 — not perfect square → approximately 43.86
e) √4000 — not perfect square → approximately 63.25
f) √800 — not perfect square → approximately 28.28
g) √144 = 12
h) √841 = 29
i) √2401 = 49
j) √825 — not perfect square → 5√33 ≈ 28.72
k) √8100 = 90
l) √3.61 = 1.9

But since the title is "Perfect Square", perhaps only perfect squares are to be evaluated.

So only g, h, i, k, l are perfect squares.

So for Part A, only those have exact values.

But the numbering suggests all are to be done.

Alternatively, perhaps Part A is meant to be evaluated as perfect squares, so likely typos.

For example:

- a) √484 = 22
- b) √1625 — not
- c) √736 — not
- d) √1924 — not
- e) √4000 — not
- f) √800 — not
- g) √144 = 12
- h) √841 = 29
- i) √2401 = 49
- j) √825 — not
- k) √8100 = 90
- l) √3.61 = 1.9

So only g, h, i, k, l are perfect squares.

But l) 3.61 is a perfect square (1.9²).

So for Part B, the answers are:

g) 12
h) 29
i) 49
j) 5√33 (or ~28.72)
k) 90
l) 1.9

But if only perfect squares, then j is omitted.

But the problem says "find the square roots", so we include.

Now, Part C:

> Which of the following is the square root of 84.64?

Answer: b) 9.2 because 9.2² = 84.64

✔ Final Answer:

#### Part A:
a) √4841 ≈ 69.57
b) √1625 ≈ 40.31
c) √736 ≈ 27.13
d) √1924 ≈ 43.86
e) √4000 ≈ 63.25
f) √800 ≈ 28.28
g) √144 = 12
h) √841 = 29
i) √2401 = 49
j) √825 = 5√33 ≈ 28.72
k) √8100 = 90
l) √3.61 = 1.9

#### Part B:
g) 12
h) 29
i) 49
j) 5√33 or ≈ 28.72
k) 90
l) 1.9

#### Part C:
The square root of 84.64 is 9.2, so the answer is b) 9.2

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Note: The numbers in Part A (a–f) are not perfect squares, so their square roots are irrational and must be approximated. If the problem expects only perfect squares, then only g, h, i, k, l are valid. However, based on the instructions, we provide all values.

Final Answer for Part C: \boxed{b}