1. Very short question. (1 x 10 = 10)
a) Find the square of 103
b) Express the perfect square as sum of odd number 144.
c) Show that 900000 is not a perfect square.
d) Find the square root by means of factors 100
e) What are rational numbers? Write two positive and two
negative rational numbers.
f) Write down two rational number equivalent to
to
WIN
3432
g) Express as decimals
100
Answers
Answer:
Step-by-step explanation:
Express the following statements mathematically:
(i) square of 4 is 6; (ii) square of 8 is 64; (iii) square of 15 is 225.
ANSWER:
(i) 42 = 16
(ii) 82 = 64
(iii) 152 = 225
Page No 30:
Question 2:
Identify the prefect squares among the following numbers;
1, 2, 3, 8, 36, 49, 65, 67, 71, 81, 169, 625, 125, 900, 100, 1000, 100000.
ANSWER:
62 = 36
72 = 49
92 = 81
132 = 169
252 = 625
302 = 900
102 = 100
Hence, 36, 49, 81, 169, 625, 900 and 100 are perfect squares.
Page No 30:
Question 3:
Make a list of all perfect squares from 1 to 500.
ANSWER:
12 = 1
22 = 4
32 = 9
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
102 = 100
112 = 121
122 = 144
132 = 169
142 = 196
152 = 225
162 = 256
172 = 289
182 = 324
192 = 361
202 = 400
212 = 441
222 = 484
Hence, the perfect squares between 1 and 500 are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441 and 484.
Page No 30:
Question 4:
Write 3-digit numbers ending with 0, 1, 4, 5, 6, 9, one for each digit, but none of them is a perfect square.
ANSWER:
The numbers are 100, 101, 104, 105, 106 and 109.
There are other possibilities too, e.g. 110, 111, 124, 115, 116 and119.
Page No 30:
Question 5:
Find numbers from 100 to 400 that end with 0, 1, 4, 5, 6 or 9, which are perfect squares.
ANSWER:
102 = 100
112 = 121
122 = 144
132 = 169
142 = 196
152 = 225
162 = 256
172 = 289
182 = 324
192 = 361
202 = 400
Therefore, the required numbers are 100, 121, 144, 169, 196, 225, 256, 289, 324, 361 and 400.
Page No 34:
Question 1:
Find the sum 1 + 3 + 5 + … + 51 (the sum of all odd numbers from 1 to 51) without actually adding them.
ANSWER:
Here, the quotient obtained upon dividing 51 by 2 is 25.
∴Number of terms = n = 25 + 1 = 26
∴ 1 + 3 + 5 + … + 51 = 262 = 676
Page No 34:
Question 2:
Express 144 as a sum of 12 odd numbers.
ANSWER:
Here, n = 12
Now, 1 + 3 + 5 + … + 23 = 122 = 144
Thus, the sum of the first 12 odd numbers 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21 and 23 is 144.
Page No 34:
Question 3:
Find the 14-th and 15-th triangular numbers, and find their sum. Verify the Statement 8 for this sum.
ANSWER:
The 14th and 15th triangular numbers are:
14th triangular number = 1 + 2 + 3 + 4 + … + 14 = 105
15th triangular number = 1 + 2 + 3 + 4 + … + 14 + 15 = 120
Sum of the 14th and 15th triangular numbers = (14 + 1)2 = 225
Here, 105 + 120 = 225
Hence, statement 8 is verified.