Class 8 Squares and Square Roots Chapter 6 worksheet - Free Printable

Let's analyze each statement one by one and determine whether it is true or false.

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Statement a) 369 is a perfect square number.

- A perfect square number is a number that can be expressed as \( n^2 \) for some integer \( n \).
- To check if 369 is a perfect square, we find its square root:
\[
\sqrt{369} \approx 19.21
\]
Since the square root of 369 is not an integer, 369 is not a perfect square.
- Answer: False

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Statement b) The sum of the first \( n \) odd natural numbers is \( n^2 \).

- The sum of the first \( n \) odd natural numbers is given by the formula:
\[
1 + 3 + 5 + \cdots + (2n-1) = n^2
\]
- This is a well-known mathematical property.
- Answer: True

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Statement c) There are 13 non-perfect square numbers lie between \( 6^2 \) and \( 7^2 \).

- First, calculate \( 6^2 \) and \( 7^2 \):
\[
6^2 = 36, \quad 7^2 = 49
\]
- The numbers between 36 and 49 are:
\[
37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48
\]
- Count these numbers:
\[
48 - 37 + 1 = 12
\]
- There are 12 numbers in total, and none of them are perfect squares (since the next perfect square after 36 is 49).
- Answer: False

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Statement d) There are 26 non-perfect square numbers lie between \( 12^2 \) and \( 13^2 \).

- First, calculate \( 12^2 \) and \( 13^2 \):
\[
12^2 = 144, \quad 13^2 = 169
\]
- The numbers between 144 and 169 are:
\[
145, 146, 147, \ldots, 168
\]
- Count these numbers:
\[
168 - 145 + 1 = 24
\]
- There are 24 numbers in total, and none of them are perfect squares (since the next perfect square after 144 is 169).
- Answer: False

---

Statement e) The square of an odd number is an even number.

- Let \( n \) be an odd number. Then \( n \) can be written as \( n = 2k + 1 \) for some integer \( k \).
- The square of \( n \) is:
\[
n^2 = (2k + 1)^2 = 4k^2 + 4k + 1 = 2(2k^2 + 2k) + 1
\]
- Since \( 2(2k^2 + 2k) + 1 \) is of the form \( 2m + 1 \) (where \( m = 2k^2 + 2k \)), it is an odd number.
- Answer: False

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Statement f) The square of an even number is an even number.

- Let \( n \) be an even number. Then \( n \) can be written as \( n = 2k \) for some integer \( k \).
- The square of \( n \) is:
\[
n^2 = (2k)^2 = 4k^2 = 2(2k^2)
\]
- Since \( 2(2k^2) \) is of the form \( 2m \) (where \( m = 2k^2 \)), it is an even number.
- Answer: True

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Statement g) There are two integral square roots in a perfect square.

- A perfect square \( n^2 \) has two square roots: \( n \) and \( -n \).
- For example, the square roots of 16 are \( 4 \) and \( -4 \).
- Answer: True

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Statement h) The smallest perfect which is divisible by 4 and 5 is 300.

- A number divisible by both 4 and 5 must be divisible by their least common multiple (LCM).
- The LCM of 4 and 5 is:
\[
\text{LCM}(4, 5) = 20
\]
- The smallest perfect square divisible by 20 must be a multiple of \( 20^2 = 400 \).
- Therefore, the smallest perfect square divisible by 4 and 5 is 400, not 300.
- Answer: False

---

Statement i) The number of digits in the square root of 42025 is 0.

- First, find the square root of 42025:
\[
\sqrt{42025} = 205
\]
- The number 205 has 3 digits.
- Answer: False

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Statement j) The length of the side of a square of area \( 625 \, \text{m}^2 \) is 20 m.

- The area of a square is given by \( \text{side}^2 \).
- If the area is 625, then:
\[
\text{side} = \sqrt{625} = 25
\]
- The length of the side is 25 m, not 20 m.
- Answer: False

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Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{a) False} & \text{b) True} \\
\text{c) False} & \text{d) False} \\
\text{e) False} & \text{f) True} \\
\text{g) True} & \text{h) False} \\
\text{i) False} & \text{j) False} \\
\end{array}
}
\]