Students often refer to Kerala State Syllabus SCERT Class 8 Maths Solutions and Class 8 Maths Chapter 1 Squares Questions and Answers Notes Pdf to clear their doubts.
SCERT Class 8 Maths Chapter 1 Solutions Squares
Class 8 Kerala Syllabus Maths Solutions Chapter 1 Squares Questions and Answers
Squares Class 8 Questions and Answers Kerala Syllabus
Perfect Squares (Page No. 11)
Question 1.
Calculate the squares given below.
(i) 642
(ii) 352
(iii) 472
(iv) 532
(v) 882
Answer:
(i) 642
642 = 602 + (2 × 60 × 4) + 42
= 3600 + 480 + 16
= 4096
(ii) 352
352 = 302 + (2 × 30 × 5) + 52
= 900 + 300 + 25
= 1225
(iii) 472
472 = 402 + (2 × 40 × 7) + 72
= 1600 + 560 + 49
= 2209
(iv) 532
532 = 502 + (2 × 50 × 3) + 32
= 2500 + 300 + 9
= 2809
(v) 882
882 = 802 + (2 × 80 × 8) + 82
= 6400 + 1280 + 64
= 7744
Decimal Squares (Page No. 13)
Question 1.
Find the squares of the numbers below:
(i) 2.3
(ii) 8.7
(iii) 10.1
(iv) 12.5
(v) 15.7
Answer:
(i) 2.32 = 22 + 2 × 2 × 0.3 + (0.3)2
= 4 + 1.2 + 0.09
= 5.29
(ii) 8.72 = 82 + 2 × 8 × 0.7 + (0.7)2
= 64 + 11.2 + 0.49
= 75.69
(iii) 10.12 = 102 + 2 × 10 × 0.1 + (0.1)2
= 100 + 2 + 0.01
= 102.01
(iv) 12.52 = 122 + 2 × 12 × 0.5 + (0.5)2
= 144 + 12 + 0.25
= 156.25
(v) 15.72 = 152 + 2 × 15 × 0.7 + (0.7)2
= 225 + 21 + 0.49
= 246.49
Class 8 Maths Chapter 1 Kerala Syllabus Squares Questions and Answers
Class 8 Maths Squares Questions and Answers
Calculate the squares given below.
Question 1.
702 = _____
Answer:
702 = 70 × 70
= 7 × 10 × 7 × 10
= 7 × 7 × 10 × 10
= 49 × 100
= 4900
Question 2.
712 = _____
Answer:
712 = 702 + 2 × 70 × 1 + 12
= 4900 + 140 + 1
= 5041
Question 3.
722 = _____
Answer:
722 = 702 + 2 × 70 × 2 + 22
= 4900 + 280 + 4
= 5184
Question 4.
752 = _____
Answer:
752 = 7 × 8 | 25 = 5625
Question 5.
8.52 = _____
Answer:
8.52 = 8 × 9 + \(\frac {1}{4}\)
= 72 + 0.25
= 72.25
Question 6.
7.42 = _____
Answer:
7.42 = 72 + 2 × 7 × 0.4 + (0.4)2
= 49 + 5.6 + 0.16
= 54.76
Question 7.
7.62 = _____
Answer:
7.62 = 72 + 2 × 7 × 0.6 + (0.6)2
= 49 + 8.4 + 0.36
= 57.76
Question 8.
75.42 = _____
Answer:
75.42 = 752 + 2 × 75 × 0.4 + (0.4)2
= 5625 + 60 + 0.16
= 5685.16
Question 9.
8.252 = _____
Answer:
8.252 = 82 + \(\frac {8}{2}\) + 0.0625
= 64 + 4 + 0.0625
= 68.0625
Question 10.
10.252 = _____
Answer:
10.252 = 102 + \(\frac {10}{2}\) + 0.0625
= 100 + 5 + 0.0625
= 105.0625
Question 11.
6.252 = _____
Answer:
6.252 = 62 + \(\frac {6}{2}\) + 0.0625
= 36 + 3 + 0.0625
= 39.0625
Question 12.
100.252 = _____
Answer:
100.252 = 1002 + \(\frac {100}{2}\) + 0.0625
= 10000 + 50 + 0.0625
= 10050.0625
Class 8 Maths Chapter 1 Notes Kerala Syllabus Squares
→ The digit in the ones place of a perfect square can only be any of these numbers: 0, 1, 4, 5, 6, or 9.
→ If a number ends in 5. The digit in the ones place of its square should be 5, and the digit in its tens place should be 2.
→ The square of an even number is always even.
→ The square of an odd number is always odd.
→ The number of factors of a perfect square is odd.
→ In the first 100 natural numbers, there are 10 perfect squares, and in the first 1000 natural numbers, there are 31 perfect squares.
A perfect square is a number that is obtained by multiplying a natural number by itself. For example, when we multiply 4 by 4, we get 16. So 16 is called the perfect square. Perfect squares are easy to recognize and have many unique patterns and properties. They are always positive, and their square roots are always natural numbers. These numbers appear frequently in mathematics, especially in geometry, like calculating the area of a square, and in algebra. In this chapter, you will learn how to find the square of an integer. And also discuss how to find the square of a decimal number.
Perfect Squares
The squares of natural numbers 1, 2, 3, … are called perfect squares.
Multiplication of two-digit numbers.
11 × 11
In another form,
11 × 11 = 100 + (10 + 10) + 1
That means,
112 = 102 + 2 × 10 + 12 = 121
Similarly, the square of 12
12 × 12
12 × 12 = 100 + 20 + 20 + 4
= 102 + 2 × 20 + 22
= 144
Without drawing the cells, we can write them like this,
132 = 102 + 2 × 30 + 32 = 169
142 = 102 + 2 × 40 + 42 = 196
Square of 20 = 20 × 20
= 2 × 10 × 2 × 10
= 2 × 2 × 10 × 10
= 4 × 100
= 400
Square of 212
2122 = 2002 + 2 × 200 × 12 + 122
= 40000 + 4800 + 144
= 44944
Square of 386
3862 = 3002 + 2 × 300 × 86 + 862
= 90000 + 51600 + 7396
= 148996
Worksheet – 1
Calculate the squares given below.
(i) 24
(ii) 56
(iii) 76
(iv) 35
(v) 91
(vi) 101
(vii) 211
(viii) 912
Answer:
(i) 576
(ii) 3136
(iii) 5776
(iv) 1225
(v) 8281
(vi) 10201
(vii) 44521
(viii) 831744
Square of 30 = 30 × 30
= 3 × 10 × 3 × 10
= 9 × 100
= 900
Square of 40 = 4 × 4 × 100
= 16 × 100
= 1600
Square of 25
25 × 25 = 202 + 2 × 20 × 5 + 52
252 = 400 + 200 + 25
252 = 625
52 × 52 = 502 + 2 × 50 × 2 + 22
522 = 2500 + 200 + 4
522 = 2704
87 × 87 = 802 + 2 × 80 × 7 + 72
872 = 6400 + 1120 + 49
872 = 7569
Simplest method to calculate the square of integers that end in 5:
For example:
352 = 302 + 2 × 30 × 5 + 52
= 900 + 300 + 25
= 1225
In this answer 1225, if we remove the last two digits 25 we get the remaining as 12.
12 | 25
The 12 is 3 × 4.
We can check this in other numbers also.
For example:
4 | 52 = 20 (4 × 5) | 25
6 | 52 = 6 × 7 | 25 = 4225
9 | 52 = 9 × 10 | 25 = 9025
1052 = 10 × 11 | 25 = 11025
2952 = 29 × 30 | 25 = 87025
10052 = 100 × 101 | 25 = 1010025
The square of the integer ending in 5 is the multiple of the number of tens (the number obtained after removing 5 from it), with the next natural number, and joining the square of 5 with this.
Decimal Squares
Square of 15 is 152 = 225
Then 1.5 × 1.5 = \(\frac{15}{10} \times \frac{15}{10}\)
= \(\frac {225}{100}\)
= 2.25
If the length of the side of a square is 2.3 metres. Find its area.
Answer:
Area = side × side
= 2.3 × 2.3
= \(\frac{23^2}{100}\)
= \(\frac {529}{100}\)
= 5.29 sq.m
This multiplication can also be considered as a rectangle math problem
3.72 = 3.7 × 3.7
= 32 + 2 × 3 × 0.7 + (0.7)2
= 9 + 4.2 + 0.49
= 13.69
4.32 = 4.3 × 4.3
= 42 + 2 × 4 × 0.3 + (0.3)2
= 16 + 2.4 + 0.09
= 18.49
Worksheet – 2
Calculate the squares given below.
Question 1.
6.82
Answer:
6.82 = 6.8 × 6.8
= 62 + 2 × 6 × 0.8 + (0.8)2
= 36 + 9.6 + 0.64
= 46.24
Question 2.
12.32
Answer:
12.32 = 12.3 × 12.3
= 122 + 2 × 12 × 0.3 + (0.3)2
= 144 + 7.2 + 0.09
= 151.29
Question 3.
30.52
Answer:
30.52 = 30.5 × 30.5
= 302 + 2 × 30 × 0.5 + (0.5)2
= 900 + 30 + 0.25
= 930.25
Simplest method to calculate the square of a number with the decimal part 0.5:
3.52 = 3.5 × 3.5
= 32 + 2 × 3 × 0.5 + (0.5)2
= 9 + 3 + 0.25
= 12.25
7.52 = 72 + 2 × 7 × 0.5 + (0.5)2
= 72 + 7 + 0.25
= 56.25
10.52 = 102 + 10 + 0.25 = 110.25
50.52 = 502 + 50 + 0.25 = 2550.25
We can see this in another form,
3.52 = 3 × 4 + 0.25 = 12.25
7.52 = 7 × 8 + 0.25 = 56.25
10.52 = 10 × 11 + 0.25 = 110.25
If the decimal part is 0.25:
For example:
2.252 = 22 + 2 × 2 × 0.25 + (0.25)2
= 4 + 1 + 0.0625
= 5.0625
3.252 = 32 + 2 × 3 × 0.25 + (0.25)2
= 9 + 1.5 + 0.0625
= 10.5625
If we consider the right side first,
Square of the integer + half of the integer + square of 0.25
Worksheet – 3
Question 1.
Find the square of 12.25.
Answer:
12.25 = Square of 12 + half of 12 + 0.0625
= 144 + 6 + 0.0625
= 150.0625
Question 2.
Square of 30.25.
Answer:
30.25 = Square of 30 + half of 30 + 0.0625
= 900 + 15 + 0.0625
= 915.0625