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By which smallest number 48 must be divided so as to make it a perfect square ?
- a)2
- b)3
- c)6
- d)4
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
By which smallest number 48 must be divided so as to make it a perfect...
By Prime factorisation, we have 48=2*2*2*2*3. We have two pairs of 2 but no pair of 3. Hence 48 must be divided by 3 to make it a perfect square.
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By which smallest number 48 must be divided so as to make it a perfect...
First you do the prime factorisation of 48
second find the different number and the number is 3 so the 48 multiply by 3 so the perfect square is 144
and this one was correct
second find the different number and the number is 3 so the 48 multiply by 3 so the perfect square is 144
and this one was correct
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By which smallest number 48 must be divided so as to make it a perfect...
To find the smallest number by which 48 must be divided in order to make it a perfect square, we need to analyze the prime factors of 48.
Prime Factorization of 48:
48 can be written as the product of its prime factors: 2 x 2 x 2 x 2 x 3.
- The prime factor 2 appears four times in the factorization, while the prime factor 3 appears once.
To make 48 a perfect square, we need to pair up the prime factors in such a way that each pair has an even exponent. In other words, the exponents of all the prime factors should be divisible by 2.
Pairing up the prime factors:
- We can pair up two 2's to get 2 x 2 = 4, which is a perfect square.
- The remaining two 2's cannot be paired up, so they will be left alone.
- The prime factor 3 cannot be paired up either.
To make the remaining two 2's a perfect square, we need to divide 48 by 2 x 2 = 4.
Therefore, the smallest number by which 48 must be divided to make it a perfect square is 4.
Hence, the correct answer is option B) 4.
Prime Factorization of 48:
48 can be written as the product of its prime factors: 2 x 2 x 2 x 2 x 3.
- The prime factor 2 appears four times in the factorization, while the prime factor 3 appears once.
To make 48 a perfect square, we need to pair up the prime factors in such a way that each pair has an even exponent. In other words, the exponents of all the prime factors should be divisible by 2.
Pairing up the prime factors:
- We can pair up two 2's to get 2 x 2 = 4, which is a perfect square.
- The remaining two 2's cannot be paired up, so they will be left alone.
- The prime factor 3 cannot be paired up either.
To make the remaining two 2's a perfect square, we need to divide 48 by 2 x 2 = 4.
Therefore, the smallest number by which 48 must be divided to make it a perfect square is 4.
Hence, the correct answer is option B) 4.
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By which smallest number 48 must be divided so as to make it a perfect square ?a)2b)3c)6d)4Correct answer is option 'B'. Can you explain this answer?
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