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NCERT Solutions · Maths Ch 1
A Square and A Cube
14 questions · 2 exercises
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Ex 1.1
Ex 1.2
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 1.1 · 9 QUESTIONS
Squares
Q1
Which of the following numbers are not perfect squares? (i) 2032 (ii) 2048 (iii) 1027 (iv) 1089
(2 marks)
Q2
Which one among 64², 108², 292², 36² has last digit 4?
(2 marks)
Q3
Given 125² = 15625, what is the value of 126²? (i) 15625 + 126 (ii) 15625 + 26² (iii) 15625 + 253 (iv) 15625 + 251 (v) 15625 + 25²
(2 marks)
Q4
Find the length of the side of a square whose area is 441 m².
(2 marks)
Q5
Find the smallest square number that is divisible by each of the following numbers: 4, 9, and 10.
(2 marks)
Q6
Find the smallest number by which 9408 must be multiplied so that the product is a perfect square. Find the square root of the product.
(2 marks)
Q7
How many numbers lie between the squares of the following numbers? (i) 16 and 17 (ii) 99 and 100
(1 mark)
Q8
In the following pattern, fill in the missing numbers: 1² + 2² + 2² = 3²; 2² + 3² + 6² = 7²; 3² + 4² + 12² = 13²; 4² + 5² + 20² = (___)²; 9² + 10² + (___)² = (___)²
(2 marks)
Q9
How many tiny squares are there in the following picture? Write the prime factorisation of the number of tiny squares.
Figure: a 9 × 9 arrangement of tiles (alternately straight and tilted); every tile is a 5 × 5 grid of tiny squares.
(3 marks)
2
EXERCISE 1.2 · 5 QUESTIONS
Cubes
Q1
Find the cube roots of 27000 and 10648.
(2 marks)
Q2
What number will you multiply by 1323 to make it a cube number?
(2 marks)
Q3
State true or false. Explain your reasoning. (i) The cube of any odd number is even. (ii) There is no perfect cube that ends with 8. (iii) The cube of a 2-digit number may be a 3-digit number. (iv) The cube of a 2-digit number may have seven or more digits. (v) Cube numbers have an odd number of factors.
(2 marks)
Q4
You are told that 1331 is a perfect cube. Can you guess without factorisation what its cube root is? Similarly, guess the cube roots of 4913, 12167, and 32768.
(3 marks)
Q5
Which of the following is the greatest? Explain your reasoning. (i) 67³ – 66³ (ii) 43³ – 42³ (iii) 67² – 66² (iv) 43² – 42²
(2 marks)