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Unit Test : Square and Square Roots | Mathematics (Maths) Class 8 PDF Download

Time: 1 hour

M.M.: 30

Attempt all questions.

Question numbers 1 to 5 carry 1 mark each.

Question numbers 6 to 8 carry 2 marks each.

Question numbers 9 to 11 carry 3 marks each.

Question numbers 12 & 13 carry 5 marks each.

Q1: A rectangular field has a length of 24 meters and a width of 7 meters. Calculate the diagonal of the field using the Pythagorean theorem and verify if the result is correct. (1 Mark)
Q2: Use the identity and find the square of 189. (1 Mark)

(a – b)²= a² – 2ab + b²
Q3: The sum of the first 5 odd natural numbers is equal to the square of which number? (1 Mark)
(i) 2
(ii) 3
(iii) 4
(iv) 5
Q4: Find the number of non-square numbers between the squares of 10 and 11. (1 Mark)
(i) 21
(ii) 19
(iii) 20
(iv) 18
Q5: The sum of two consecutive triangular numbers is a square number. Find the sum of 10 and 11 triangular numbers and verify this statement. (1 Mark)
Q6: Find the smallest square number that is divisible by each of the numbers 8, 15 and 20. (2 Marks)
Q7: Show that the sum of two consecutive natural numbers is 13². (2 Marks)
Q8: How many numbers lie between squares of the following numbers? (2 Marks)
(i) 12 and 13
(ii) 25 and 26
Q9: Find the smallest whole number by which 1008 should be multiplied so as to get a perfect square number. Also, find the square root of the square number so obtained. (3 Marks)
Q10: Write a Pythagorean triplet whose one member is: (3 Marks)
(i) 6
(ii) 14
(iii) 16
(iv) 18
Q11. Find the square roots of 100 and 169 by the method of repeated subtraction. (3 Marks)
Q12: 2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row. (5 Marks)
Q13: Find the least number which must be added to 1750 so as to get a perfect square. Also, find the square root of the obtained number. (5 Marks)
You can find the solutions of this Unit Test here: Unit Test (Solution): Square and Square Roots

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FAQs on Unit Test : Square and Square Roots - Mathematics (Maths) Class 8

1. What is the difference between a square and a square root?

Ans.A square is the result of multiplying a number by itself (e.g., \(3^2 = 9\)), while a square root is a value that, when multiplied by itself, gives the original number (e.g., \(\sqrt{9} = 3\)).

2. How can I determine the square of a number?

Ans.To find the square of a number, simply multiply the number by itself. For example, to find the square of 5, calculate \(5 \times 5 = 25\).

3. What is the significance of square roots in mathematics?

Ans.Square roots are important in mathematics as they help solve equations, particularly in algebra and geometry, allowing us to find original values from their squares.

4. Can you provide an example of how to calculate a square root?

Ans.To calculate a square root, you can use the prime factorization method or a calculator. For example, to find \(\sqrt{16}\), you can recognize that \(4 \times 4 = 16\), so \(\sqrt{16} = 4\).

5. Are there any real-world applications of squares and square roots?

Ans.Yes, squares and square roots are used in various fields such as architecture for area calculations, physics for solving equations, and finance for determining interest rates and investment growth.

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