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 a ² and is given by a ² = a x a.
That is, the square of a number is obtained by multiplying it by itself.
If a x a = b i.e. a ² = 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) 3 ² = 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

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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
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