A Square and A Cube
Class 8 · Mathematics Part 1 · 29 Questions
Given 125² = 15625, what is the value of 126²?
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
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
Write the locker numbers that remain open. [Condition: Each person is assigned a number from 1 to 100. Person 1 opens every locker. Person 2 toggles every 2nd locker (i.e., closes it if it is open, opens it if it is closed). Person 3 toggles every 3rd locker (3rd, 6th, 9th, … and so on). Person 4 toggles every 4th locker (4th, 8th, 12th, … and so on). This continues until all 100 get their turn. In the end, only some lockers remain open. The open lockers reveal the code to the fortune in the safe.]
Write 5 numbers such that you can determine by looking at their units digit that they are not squares.
Which of the following numbers have the digit 6 in the units place? (i) 38² (ii) 34² (iii) 46² (iv) 56² (v) 74² (vi) 82²
If a number contains 3 zeros at the end, how many zeros will its square have at the end?
What can you say about the parity of a number and its square?
Find 36², given that 35² = 1225.
Find how many numbers lie between two consecutive perfect squares. Do you notice a pattern?
Answer the following questions:
Find whether 1156 and 2800 are perfect squares using prime factorisation.