1. Find the square of the following numbers:
a) 7
b) 12
c) 18
2. Write the following in square form and find the value:
a) $9 \times 9$
b) $15 \times 15$
3. Find the value of:
a) $16^2$
b) $23^2$
c) $25^2$
4. Complete the table: | Number | Square | | :— | :— | | 11 | ____ | | 14 | ____ | | 19 | ____ |
7. Match the following: | Number | Square | | :— | :— | | 20 | 400 | | 25 | 625 | | 30 | 900 |
5. Find the square of the following multiples of 10:
a) 30
b) 60
c) 90
6. Without using a calculator, find:
a) $21^2$
b) $22^2$
c) $23^2$
8. Write True or False:
a) $10^2 = 100$
b) $15^2 = 215$
c) $30^2 = 900$
9. Find the square roots of:
a) 81
b) 144
c) 400
10. If the square of a number is 729, find the number.
1. Find the square of the following numbers:
a) 7: $7 \times 7 = 49$.
b) 12: $12 \times 12 = 144$.
c) 18: $18 \times 18 = 324$.
Explanation: To find the “square” of a number, you multiply the number by itself.
2. Write the following in square form and find the value:
a) $9 \times 9$: Square form is $9^2$. The value is 81.
b) $15 \times 15$: Square form is $15^2$. The value is 225.
Explanation: “Square form” uses an exponent of 2 (a superscript) to show the number is being multiplied by itself once.
3. Find the value of:
a) $16^2$: $16 \times 16 = 256$.
b) $23^2$: $23 \times 23 = 529$.
c) $25^2$: $25 \times 25 = 625$.
4. Complete the table:
11: $11^2 = 121$.
14: $14^2 = 196$.
19: $19^2 = 361$.
5. Find the square of the following multiples of 10:
a) 30: $30 \times 30 = 900$.
b) 60: $60 \times 60 = 3,600$.
c) 90: $90 \times 90 = 8,100$.
Explanation: A quick trick for multiples of 10 is to square the non-zero digit and then double the number of zeros (e.g., for $30^2$, $3^2 = 9$ and one zero becomes two zeros, resulting in 900).
6. Without using a calculator, find:
a) $21^2$: $21 \times 21 = 441$.
b) $22^2$: $22 \times 22 = 484$.
c) $23^2$: $23 \times 23 = 529$.
7. Match the following:
20 matches with 400 ($20 \times 20$).
25 matches with 625 ($25 \times 25$).
30 matches with 900 ($30 \times 30$).
8. Write True or False:
a) $10^2 = 100$: True.
b) $15^2 = 215$: False. (The correct value is 225).
c) $30^2 = 900$: True.
9. Find the square roots of:
a) 81: The square root is 9, because $9^2 = 81$.
b) 144: The square root is 12, because $12^2 = 144$.
c) 400: The square root is 20, because $20^2 = 400$.
Explanation: A square root is the inverse of squaring; it asks “what number multiplied by itself gives this result?”
10. If the square of a number is 729, find the number:
Answer: 27.
Explanation: We need to find $\sqrt{729}$. Since $20^2 = 400$ and $30^2 = 900$, the number must be between 20 and 30. Because it ends in 9, the last digit is likely 3 or 7 ($3 \times 3 = 9$ or $7 \times 7 = 49$). Testing 27: $27 \times 27 = 729$.