Back to Ganita Prakash
Class 8 Mathematics
Chapter 1 Solutions — A Square and a Cube
Open Solutions PDFReads in your browser→Also seeTextbook page→Solutions
Overview
Step-by-step NCERT solutions for A Square and a Cube (Chapter 1, NCERT Class 8 Mathematics) — the full working for every question, not just the final answer. You can also read the A Square and a Cube textbook chapter.
Solved
What these solutions cover
All 14 questions in A Square and a Cube are solved in the PDF. Here's what's inside, exercise by exercise:
Square Numbers and Square Roots
- Which of the following numbers are not perfect squares?
- (i) 2032
- (ii) 2048
- (iii) 1027
- (iv) 1089
- Which one among 64², 108², 292², 36² has last digit 4?
- Given 125² = 15625, what is the value of 126²?
- (i) 15625 + 126
- (ii) 15625 + 26²
- (iii) 15625 + 253
- (iv) 15625 + 251
- (v) 15625 + 51²
- Find the length of the side of a square whose area is 441 m².
- Find the smallest square number that is divisible by each of the following numbers: 4, 9, and 10.
- 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.
- How many numbers lie between the squares of the following numbers?
- (i) 16 and 17
- (ii) 99 and 100
- 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
- How many tiny squares are there in the following picture? Write the prime factorisation of the number of tiny squares.
Cubic Numbers and Cube Roots
- Find the cube roots of 27000 and 10648.
- What number will you multiply by 1323 to make it a cube number?
- 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.
- 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.
- Which of the following is the greatest? Explain your reasoning.
- (i) 67³ – 66³
- (ii) 43³ – 42³
- (iii) 67² – 66²
- (iv) 43² – 42²
Keep solving
More solutions in Ganita Prakash
Explore
More NCERT Solutions for Class 8
Read the A Square and a Cube textbook chapter / PDF, or browse all NCERT Class 8 Mathematics solutions.
Solve offline with notes, solutions & mock tests
CBSE Prepmaster — free on iOS & Android