CBSE Class 8 Mental Maths Squares And Square Roots Worksheet - Free Printable

Problem: Solve the questions from the image related to squares and square roots.

#### Questions:
1. What is the square of 17?
2. Find the square of 24.
3. What is the product of two odd numbers?
4. Can we have a square number with unit digit 8?

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Solution:

#### Question 1: What is the square of 17?
To find the square of 17, we calculate \( 17^2 \):
\[
17^2 = 17 \times 17
\]
Perform the multiplication:
\[
17 \times 17 = 289
\]

Answer: \( \boxed{289} \)

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#### Question 2: Find the square of 24.
To find the square of 24, we calculate \( 24^2 \):
\[
24^2 = 24 \times 24
\]
Perform the multiplication:
\[
24 \times 24 = 576
\]

Answer: \( \boxed{576} \)

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#### Question 3: What is the product of two odd numbers?
The product of two odd numbers is always an odd number. This is because:
- An odd number can be expressed as \( 2n + 1 \), where \( n \) is an integer.
- The product of two odd numbers \( (2a + 1) \) and \( (2b + 1) \) is:
\[
(2a + 1)(2b + 1) = 4ab + 2a + 2b + 1 = 2(2ab + a + b) + 1
\]
This expression is of the form \( 2k + 1 \), which is an odd number.

Answer: The product of two odd numbers is always an odd number.

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#### Question 4: Can we have a square number with unit digit 8?
To determine if a square number can have a unit digit of 8, we examine the unit digits of the squares of all possible digits (0 through 9):

- \( 0^2 = 0 \) (unit digit is 0)
- \( 1^2 = 1 \) (unit digit is 1)
- \( 2^2 = 4 \) (unit digit is 4)
- \( 3^2 = 9 \) (unit digit is 9)
- \( 4^2 = 16 \) (unit digit is 6)
- \( 5^2 = 25 \) (unit digit is 5)
- \( 6^2 = 36 \) (unit digit is 6)
- \( 7^2 = 49 \) (unit digit is 9)
- \( 8^2 = 64 \) (unit digit is 4)
- \( 9^2 = 81 \) (unit digit is 1)

From the above, the possible unit digits of a square number are: \( 0, 1, 4, 5, 6, 9 \). The digit 8 is not in this list.

Answer: No, we cannot have a square number with a unit digit of 8.

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Final Answers:

1. \( \boxed{289} \)
2. \( \boxed{576} \)
3. The product of two odd numbers is always an odd number.
4. \( \boxed{\text{No}} \)