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RS Aggarwal Solutions Class 8 Maths Chapter 3 Squares And Square Roots
RS Aggarwal Solutions Class 8 Maths Chapter 3 Squares And Square Roots – Overview
- Definitions
The value generated by multiplying the number by itself is called the Square of a number.
The value that, when multiplied by itself, gives the original value, is the square root of a number.
For example:
(6)² = 36
Square of 6 is 36 whereas 6 is the square root of 36. Therefore, the concept of the square and square root are opposite.
- Properties Of A Square Number
- Square of any number gives a positive number.
- Square of 1 is 1.
- Square of 0 is 0.
- The Square of a number under the root gives the same number as the number under the root.
- For example (√3)² = 3
There are 2 ways to find the square root of a number correctly:
- Prime Factorisation Method
- Using Long Division Method
-
Squares and Square Roots of Numbers From 1 to 50
Number |
Square of Number |
Square Root of Number |
1 |
1 |
1.000 |
2 |
4 |
1.414 |
3 |
9 |
1.732 |
4 |
16 |
2.000 |
5 |
25 |
2.236 |
6 |
36 |
2.449 |
7 |
49 |
2.646 |
8 |
64 |
2.828 |
9 |
81 |
3.000 |
10 |
100 |
3.162 |
11 |
121 |
3.317 |
12 |
144 |
3.464 |
13 |
169 |
3.606 |
14 |
196 |
3.742 |
15 |
225 |
3.873 |
16 |
256 |
4.000 |
17 |
289 |
4.123 |
18 |
324 |
4.243 |
19 |
361 |
4.359 |
20 |
400 |
4.472 |
21 |
441 |
4.583 |
22 |
484 |
4.690 |
23 |
529 |
4.796 |
24 |
576 |
4.899 |
25 |
625 |
5.000 |
26 |
676 |
5.099 |
27 |
729 |
5.196 |
28 |
784 |
5.292 |
29 |
841 |
5.385 |
30 |
900 |
5.477 |
31 |
961 |
5.568 |
32 |
1,024 |
5.657 |
33 |
1,089 |
5.745 |
34 |
1,156 |
5.831 |
35 |
1,225 |
5.916 |
36 |
1,296 |
6.000 |
37 |
1,369 |
6.083 |
38 |
1,444 |
6.164 |
39 |
1,521 |
6.245 |
40 |
1,600 |
6.325 |
41 |
1,681 |
6.403 |
42 |
1,764 |
6.481 |
43 |
1,849 |
6.557 |
44 |
1,936 |
6.633 |
45 |
2,025 |
6.708 |
46 |
2,116 |
6.782 |
47 |
2,209 |
6.856 |
48 |
2,304 |
6.928 |
49 |
2,401 |
7.000 |
50 |
2,500 |
7.071 |
- Perfect and Imperfect Square
- Perfect Square: If a whole number is multiplied by itself to generate a given number, it is said to be a Perfect square.
Example:
25−−√=5×5−−−−√=5 - Imperfect square: If a whole number is not multiplied to generate a given number, it is an imperfect square.
Example:
13−−√=3.606
- In between Squares
Suppose the 2 consecutive squares are n² and (n+1)², then the number between them is 2n.
For example:
Find the numbers between 2² and 3².
2² = 4
3² = 9
And, n = 2
Therefore, the total numbers between 4 and 9 = 2n = 4
Therefore, the numbers are 5, 6, 7, 8.
- Pythagorean Triplet
3 positive integers a, b, c which satisfies this Pythagoras theorem a²+b²=c² is called the Pythagorean Triplet and the positive integers are called Pythagorean triples.
Example: (3, 4, 5)
By evaluating we get:
32 + 42 = 52
9 + 16 = 25
Hence, 3, 4, and 5 are the Pythagorean triples.
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