Find the least number by which each of the given number should be divided so as to get a perfect square also find the square root of the resulting number 3528 Find the least number by which of the given number should be divided so as to get a perfect square also find the square root of the resulting number
Answers
Answer:For this, we use the method called prime factorization.
Step 1 :
Find the prime factors of the given number.
Step 2 :
To find the square root, we have to group the factors as pairs.
Step 3 :
By grouping the factors as pairs, we may find some of the numbers which are being extra.These are the required numbers to be divided in order make the given number as a perfect square.
Step-by-step explanation:
Answer:
1)Firstly, factorize 3528.
3528 = 2 * 2 * 2 *3 * 3 * 7 * 7.
Now we know that a perfect square should have a pair of two prime factor.
This number has 1 pair of 2, 1 pair of 3, 1 pair of 7 and 1 alone factor 2.
Therefore, this number has a 2 less. So, 2 must be multiplied in 3528 to get a perfect square.
2)Firstly, factorize 5000.
5000 = 2 * 2 * 2 * 5 * 5 * 5 * 5.
Now we know that a perfect cube should have a pair of three prime factor.
This number has 1 pair of 2, 1 pair of 5 and 1 alone factor 5.
Therefore, this number has a 5 more. So, 5 must be divided in 5000 to get a perfect cube.
3)Firstly, factorize 180.
180 = 2 * 2 * 3 * 3 * 5.
Now we know that a perfect square should have a pair of two prime factor.
This number has 1 pair of 2, 1 pair of 3 and 1 alone factor 5.
Therefore, this number has a 5 more. So, 5 must be divided in 180 to get a perfect square.
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