Question 1

Which one among $64^2$, $108^2$, $292^2$, $36^2$ has last digit 4?

Given $125^2 = 15625$, what is the value of $126^2$?

(i) $15625 + 126$

(ii) $15625 + 26^2$

(iii) $15625 + 253$

(iv) $15625 + 251$

(v) $15625 + 51^2$

Find the length of the side of a square whose area is $441 \text{ m}^2$.

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:

(a) $4^2 + 5^2 + 20^2 = (\underline{\quad})^2$

(b) $9^2 + 10^2 + (\underline{\quad})^2 = (\underline{\quad})^2$

How many tiny squares are there in the following picture? Write the prime factorisation of the number of tiny squares.

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) $67^3 - 66^3$

(ii) $43^3 - 42^3$

(iii) $67^2 - 66^2$

(iv) $43^2 - 42^2$