Page 64 - Start Up Mathematics_8 (Non CCE)

2
fi x = 4 × 256 2 1,024
fi x = 4 256¥ = 1,024 2 512

= 22 22 22 22 22¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ = 32 2 256
2 128
= 2 × 2 × 2 × 2 × 2 2 64
256 2 32
\ One number = 32 and other number = = 8
32 2 16
2 8
2 4
2 2
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EXERCISE 3.4
1. What are the possible units digits of the square roots of the following numbers? Which of these have
even square roots?
(a) 9,604 (b) 99,225 (c) 9,96,004 (d) 15,25,225 (e) 1,06,276 (f) 1,76,400
2. Find the square root of the following using prime factorization:
(a) 576 (b) 1,444 (c) 2,401 (d) 3,364 (e) 4,761 (f) 50,625
(g) 1,35,424 (h) 2,02,500 (i) 1,80,625 (j) 5,11,225
3. In each of the following questions, find the smallest number by which it should be multiplied to get
a perfect square. Find the square root of the perfect squares so obtained.
(a) 392 (b) 216 (c) 11,045 (d) 3,698 (e) 11,094
4. In each of the following questions, find the smallest number by which it should be divided to get a
perfect square. Find the square root of the perfect squares so obtained.
(a) 4,050 (b) 17,328 (c) 53,016 (d) 38,440 (e) 5,832
5. The product of two numbers is 2916. If one number is 36 times the other, find the numbers.
6. A group of boys collected 256 marbles for some project. The contribution of each boy was equal to
the number of boys in the group. How many boys were there in the group?
2
7. The area of a square garden is 4,624 m . What is its dimension?
8. Find the square root of the following using repeated subtraction:
(a) 144 (b) 121 (c) 196 (d) 225
9. Find the least square number exactly divisible by each one of the following numbers:
(a) 8, 9, 10 (b) 20, 15, 9, 6 (c) 4, 6, 10, 18
10. Write the prime factorization of the following numbers and hence their square roots:
(a) 4,761 (b) 3,364 (c) 9,025 (d) 6,084

3. Finding Square Root of Perfect Squares by Long Division Method
756
To find the square root of large perfect square numbers, long division method
is the most convenient and easy method to adopt. 7 57 15 36
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For example, let’s find the square root of 5,71,536.
145 815
Step 1: Prepare the number by placing bars. Write 5,71,536 as 571536. 725
Step 2: Taking the first period (57), find the largest number whose square is 1506 9036
< 57. That number is 7, which forms the divisor and also the quotient. 9036
Step 3: Write the number in the space meant for the quotient and write the 0
product (square) below the first period.
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