1. Using Prime factorisation method, find which of the following numbers are perfect squares
(a) 11025
(b) 1039
(C) 6292
2) By what least number should the given number be multiplied to get a perfect square number? in
each case, find the number whose square is the new number.
(a) 3380
(b) 7623
(c) 3332
3) By what least number should the given number be divided to get a perfect square number? In each
case, find the number whose scuare is the new number:
(a) 4500
(b) 9075
(c) 7776
4) Find the largest 3 digit number which is a perfect square.
5) Find the largest 4 digit number which is a perfect square
6) Find: (a) 31 x 32 (b) 31 x 29
(c) 31 x 31
7) The students of a class arranged a picnic. Each student contributed as many rupees as the number
of students in the class. If the total contribution is 1156, find the strength of the ciass.
8) Find the square root by Division method: (a) 5329 (b) 16384 (c) 10609 (d) 66049
9) IVhat least number must be subtracted from 7250 to get a perfect square? Also find the square
root of the perfect square, so obtained.
10) Find the least number which must be added to 6203 to obtain a perfect square. Find this perfect
square and its square root
11) Evaluate: 17956
12) Find the greatest number of 5 digits which is a perfect square. Also find the square root of the
number so obtained
13) The area of square field is 60025 m. A man cycles along its boundary at 18 km/hr. in how much
time will he return to the starting point?
14) Evaluate: 16.4009
Answers
Given : Numbers (a) 11025 (b) 1039 (C) 6292
To find : Which numbers are perfect square
Solution:
11025 = 3 * 3 * 5 * 5 * 7 * 7 = 3² * 5² * 7² = 105² => perfect square
1039 is a prime number - not perfect square
6292 = 2 * 2 * 11 * 11 * 13 = 2² * 11² * 13 ( not perfect square)
3380 = 2 * 2 * 5 * 13 * 13 - multiplying by 5 will get perfect square
= (2 * 5 * 13)² = 130²
7623 = 3 * 3 * 7 * 11 * 11 multiplying by 7 will get perfect square
= (3 * 7 * 11)² = 231²
3332 = 2 * 2 * 7 * 7 * 17 multiplying by 17 will get perfect square
= (2 * 7 * 17)² = 238²
please post Question one by one
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Answer:
11025 = 3 * 3 * 5 * 5 * 7 * 7 = 3² * 5² * 7² = 105² => perfect square
1039 is a prime number - not perfect square
6292 = 2 * 2 * 11 * 11 * 13 = 2² * 11² * 13 ( not perfect square)
3380 = 2 * 2 * 5 * 13 * 13 - multiplying by 5 will get perfect square
= (2 * 5 * 13)² = 130²
7623 = 3 * 3 * 7 * 11 * 11 multiplying by 7 will get perfect square
= (3 * 7 * 11)² = 231²
3332 = 2 * 2 * 7 * 7 * 17 multiplying by 17 will get perfect square
= (2 * 7 * 17)² = 238²