RS Aggarwal Solutions Class 8 Maths Chapter 3 Squares And Square Roots (Updated For 2024)

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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

The 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

1. The square of any number gives a positive number.
2. The square of 1 is 1.
3. The square of 0 is 0.
4. The Square of a number under the root gives the same number as the number under the root.
5. For example (√3)² = 3

There are 2 ways to find the square root of a number correctly:

1. Prime Factorisation Method
2. 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

1. 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
2. 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 satisfy 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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