Squares and Square Roots
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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 |
1^{2} = 1 x 1 = 1 |
2 |
2^{2} = 2 x 2 = 4 |
3 |
3^{2} = 3 x 3 = 9 |
4 |
4 ^{2} = 4 x 4 = 16 |
5 |
5^{2} = 5 x 5 = 25 |
6 |
6^{2} = 6 x 6 = 36 |
7 |
7^{2} 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
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