3. 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
(1) 3675
(v) 9075
(ii) 2156
(vi) 7623
(iii) 3332
(vii) 3380
(iv) 2925
(viii) 2475
4. By what least number should the given number be divided to get a perfect square number?
In each case,
find the number whose squares is the new number.
Answers
Step-by-step explanation:
3 question
(i) 3675
At first,
We’ll resolve the given number into prime factors:
Hence,
3675 = 3 × 25 × 49
= 7 × 7 × 3 × 5 × 5
= (5 × 7) × (5 × 7) × 3
In the above factors only 3 is unpaired
So, in order to get a perfect square the given number should be multiplied by 3
Hence,
The number whose perfect square is the new number is as following:
= (5 × 7) × (5 × 7) × 3 × 3
= (5 × 7 × 3) × (5 × 7 × 3)
= (5 × 7 × 3)2
= (105)2
(ii) 2156
At first
We’ll resolve the given number into prime factors:
Hence,
2156 = 4 × 11 × 49
= 7 × 7 × 2 × 2 × 11
= (2 × 7) × (2 × 7) × 11
In the above factors only 11 is unpaired
So, in order to get a perfect square the given number should be multiplied by 11
Hence,
The number whose perfect square is the new number is as following:
= (2 × 7) × (2 × 7) × 11 × 11
= (2 × 7 × 11) × (2 × 7 × 11)
= (5 × 7 × 11)2
= (154)2
(iii) 3332
At first,
We’ll resolve the given number into prime factors:
Hence,
3332 = 4 × 17 × 49
= 7 × 7 × 2 × 2 × 17
= (2 × 7) × (2 × 7) × 17
In the above factors only 17 is unpaired
So, in order to get a perfect square the given number should be multiplied by 17
Hence,
The number whose perfect square is the new number is as following:
= (2 × 7) × (2 × 7) × 17 × 17
= (2 × 7 × 17) × (2 × 7 × 17)
= (2 × 7 × 17)2
= (238)2
(iv) 2925
At first,
We’ll resolve the given number into prime factors:
Hence,
2925 = 9 × 25 × 13
= 3 × 3 × 13 × 5 × 5
= (5 × 3) × (5 × 3) × 13
In the above factors only 13 is unpaired
So, in order to get a perfect square the given number should be multiplied by 13
Hence,
The number whose perfect square is the new number is as following:
= (5 × 3) × (5 × 3) × 13 × 13
= (5 × 3 × 13) × (5 × 3 × 13)
= (5 × 3 × 13)2
= (195)2
(v) 9075
At first,
We’ll resolve the given number into prime factors:
Hence,
9075 = 3 × 25 × 121
= 11 × 11 × 3 × 5 × 5
= (5 × 11) × (5 × 11) × 3
In the above factors only 3 is unpaired
So, in order to get a perfect square the given number should be multiplied by 3
Hence,
The number whose perfect square is the new number is as following:
= (5 × 11) × (5 × 11) × 3 × 3
= (5 × 11 × 3) × (5 × 11 × 3)
= (5 × 11 × 3)2
= (165)2
(vi) 7623
At first,
We’ll resolve the given number into prime factors:
Hence,
7623 = 9 × 7 × 121
= 7 × 3 × 3 × 11 × 11
= (11 × 3) × (11 × 3) × 7
In the above factors only 7 is unpaired
So, in order to get a perfect square the given number should be multiplied by 7
Hence,
The number whose perfect square is the new number is as following:
= (3 × 11) × (3 × 11) × 7 × 7
= (11 × 7 × 3) × (11 × 7 × 3)
= (11 × 7 × 3)2
= (231)2
(vii) 3380
At first,
We’ll resolve the given number into prime factors:
Hence,
3380 = 4 × 5 × 169
= 2 × 2 × 13 × 13 × 5
= (2 × 13) × (2 × 13) × 5
In the above factors only 5 is unpaired
So, in order to get a perfect square the given number should be multiplied by 5
Hence,
The number whose perfect square is the new number is as following:
= (2 × 13) × (2 × 13) × 5 × 5
= (5 × 2 × 13) × (5 × 2 × 13)
= (5 × 2 × 13)2
= (130)2
(viii) 2475
At first,
We’ll resolve the given number into prime factors:
Hence,
2475 = 11 × 25 × 9
= 11 × 3 × 3 × 5 × 5
= (5 × 3) × (5 × 3) × 11
In the above factors only 11 is unpaired
So, in order to get a perfect square the given number should be multiplied by 11
Hence,
The number whose perfect square is the new number is as following:
=(5 × 3) × (5 × 3) × 11 × 11
= (5 × 11 × 3) × (5 × 11 × 3)
= (5 × 11 × 3)2
= (165)2
4 question
In each case, find the number whose square is the new number. Thus, to get a perfect square number, the given number should be divided by 7. Hence, the number whose square is the new number = 15. Thus, to get a perfect square number, the given number should be divided by 3
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Answer:
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