Squares and Square Roots

In this section we will discuss squares and square roots.

Square of a number and square numbers
The square of a number is that number raised to the power 2.
Thus, if ‘a’ is a number, then the square of a is written as a2 and is given by a2 = a x a.
That is, the square of a number is obtained by multiplying it by itself.
If a x a = b i.e. a2 = b, then we say that the square of number a is number b or the number b is the square of number a.

For example : 1) 32 = 3 x 3= 9, so we say that the square of 3 is 9;
2) (-4)2 = -4 x -4 = 16, so we say that the square of -4 is 16;
3) (3/5)2 = (3/5) x(3/5) = 9/25 so we say that the square of (3/5) is 9/25;

Squares of some numbers are given below :
Number
Square
Number
Square
1
12 = 1 x 1 = 1
2
22 = 2 x 2 = 4
3
32 = 3 x 3 = 9
4
4 2 = 4 x 4 = 16
5
52 = 5 x 5 = 25
6
62 = 6 x 6 = 36
7
72 7 x 7 = 49
8
8 2 8 x 8 = 64
9
9 2 9 x 9 = 81
10
10 2 10 x 10 = 100
11
11 2 = 11 x 11 = 121
12
12 2 = 12 x 12 = 144
13
13 2 = 13 x 13 = 169
14
14 2 = 14 x 14 = 196
15
15 2 = 15 x 15 = 225
16
16 2 = 16 x 16 = 256
17
17 2 = 17 x 17 = 289
18
18 2 = 18 x 18 = 324
19
19 2 = 19 x 19 = 361
20
20 2 = 20 x 20 = 400
21
21 2 = 21 x 21 = 441
22
22 2 = 22 x 22 = 484
23
23 2 = 23 x 23 = 529
24
24 2 = 24 x 24 = 576
25
25 2 = 25 x 25 = 625
26
26 2 = 26 x 26 = 676
27
27 2 = 27 x 27 = 729
28
28 2 = 28 x 28 = 784
29
29 2 = 29 x 29 = 841
30
30 2 = 30 x 30 = 900
Squares and Square roots

• Introduction of Squares and Square Roots
• Perfect Squares or not
• Properties of Square Numbers
• Short cut method to find squares
• Introduction of Square Roots
• Properties of Square Roots
• Square root by Prime factorization method
• Square root by long division method
• Square root of rational numbers
• Square root of Decimals
• Square root by estimation method

Number Sense
8th grade math
Home Page