Class 8 RD Sharma Solutions – Chapter 3 Squares and Square Roots – Exercise 3.3 | Set 1
Last Updated :
06 Apr, 2021
Question 1. Find the square of the following numbers using column method. Verify the squares using the usual multiplication.
(i) 25
Solution:
Here, we will break 25 in as between one’s and ten’s position as a = 2 and b = 5. Now,
Step 1: Make 3 columns and write the values of a², 2ab, b² in these columns.
Column 1 |
Column 2 |
Column 3 |
a2 |
2ab
|
b2 |
4 |
20 |
25 |
Step 2: Underline the unit digit of b² and add its ten’s digit(if any) to 2ab.
Column 1 |
Column 2 |
Column 3 |
a2 |
2ab
|
b2 |
4 |
20 + 2 |
25 |
|
22 |
|
Step 3: Now Underline the unit digit of column 2 and add its ten’s digit(if any) to a²
Column 1 |
Column 2 |
Column 3 |
a2 |
2ab
|
b2 |
4+2 |
20+2 |
25 |
6 |
22 |
|
Step 4: Now underline the number in column 1.
Column 1 |
Column 2 |
Column 3 |
a2 |
2ab
|
b2 |
4+2 |
20+2 |
25 |
6 |
22 |
|
Step 5: Now write the underlined digits respectively as the square.
252 = 625
Now using multiplication,
252 = 25 x 25 = 625
Because we have the same result in both the methods hence our result is verified.
(ii) 37
Solution:
Here, a = 3, b = 7
Column 1 |
Column 2 |
Column 3 |
a2 |
2ab
|
b2 |
9 + 4 |
42 + 4 |
49 |
13 |
46 |
|
Now write the underlined digits respectively as the square.
372 = 1369
Now using multiplication,
372 = 37 x 37 = 1369
Because we have the same result in both the methods hence our result is verified.
(iii) 54
Solution:
Here, a = 5, b = 4.
Column 1 |
Column 2 |
Column 3 |
a2 |
2ab
|
b2 |
25+4 |
40+1 |
16 |
29 |
41 |
|
Now write the underlined digits respectively as the square.
542 = 2916
Now using multiplication,
542 = 54 x 54 = 2916
Because we have the same result in both the methods hence our result is verified.
(iv) 71
Solution:
Here, a = 7, b = 1.
Column 1 |
Column 2 |
Column 3 |
a2 |
2ab
|
b2 |
49 + 1 |
14 + 0 |
1 |
50 |
14 |
|
Now write the underlined digits respectively as the square.
712 = 5041
Now using multiplication,
712 = 71 x 71 = 5041
Because we have the same result in both the methods hence our result is verified.
(v) 96
Solution:
Here, a = 9, b = 6.
Column 1 |
Column 2 |
Column 3 |
a2 |
2ab
|
b2 |
81 + 11 |
108 + 3 |
36 |
92 |
113 |
|
Now write the underlined digits respectively as the square.
962 = 9216
Now using multiplication,
962 = 96 x 96 = 9216.
Because we have the same result in both the methods hence our result is verified.
Question 2. Find the squares of the following numbers using the diagonal method:
(i) 98
Solution:
Because, 98² = 9604
Draw a square table with equal no. of rows and columns as the no. of digits are.
Now divide each block in two parts.
Now, write the digits as depicted, and we have to store the values as provided in each block
Now Store the values as shown and add them as per the subdivision we have made, i.e., 4, 2 + 6 + 2, 7 + 1 + 7, 8 and the previous carry(i.e., take only one unit’s digit and transfer the other as carry).
Now, write the underlined(unit’s digit), as the square of the number
982 = 9604
(ii) 273
Solution:
Because, 2732 = 74529
Now, write the underlined(unit’s digit), as the square of the number
2732 = 74529
(iii) 348
Solution:
Because, 3482 = 121104
Now, write the unit’s digit as the square of 348,
3482 = 121104
(iv) 295
Solution:
Because, 2952 = 87025
Now, write each one’s digit as the square of 295,
2952 = 87025
(v) 171
Solution:
Because, 1712 = 29241
Now, write each one’s digit as the square of 171,
1712 = 29241
Question 3. Find the square of the following numbers:
(i) 127
Solution:
Here let’s take a = 120, b = 7
1272 = (120 + 7)2 = 1202 + (2 x 120 x 7) + 72
= (120 x 120) + 1680 + (7 x 7)
= 14400 + 1680 + 49
= 16129
Alternatively:
We could also take a = 100, b = 27,
1272 = 10000 + 5400 + 729 = 16129
Thus, 1272 = 16129
(ii) 503
Solution:
Here, let’s take a = 500, b = 3.
5032 = (500 + 3)2 = 5002 + (2 x 500 x 3) + 32
= 250000 + 3000 + 9
= 253009
Alternatively:
5032 = 503 x 503 = 253009
Thus, 5032 = 253009
(iii) 451
Solution:
Here, let’s take a = 400, b = 51.
4512 = (400 + 51)2 = 4002 + (2 x 400 x 51) + 512
= 160000 + 40800 + 2601
= 203401
Alternatively:
451² = 451 x 451 = 203401
451² = 203401
(iv) 862
Solution:
Here, let’s take a = 800, b = 62.
8622 = (800 + 62)2 = 8002 + (2 x 800 x 62) + 622
= 640000 + 99200 + 3844
= 743044
Alternatively:
862² = 862 x 862 = 743044
862² = 743044
(v) 265
Solution:
Here, let’s take a = 200, b = 65.
2652 = (200 + 65)2 = 2002 + (2 x 200 x 65) + 652
= 40000 + 26000 + 4225
= 70225
Alternatively:
265² = 265 x 265 = 70225
265² = 70225
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