Question

Find the least number by which 23328 should be I) multiplied to make it a perfect sqaure
ii) divided to make it a perfect square,
find the square root for new numbers in both the cases.

Answer 1

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 do not have pairs. These are the required numbers to be multiplied in order make it as a perfect square.

Example 1 :

Find the least number by which 200 must be multiplied to make it a perfect square.

Solution :

Step 1 :

Let us find the prime factors of 200 using the method prime factorization.

Step 2 :

200 = 2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ 5

Step 3 :

‘2’ remains without a pair.

Hence, 200 must be multiplied by 2 to make it a perfect square.

Example 2 :

Find the smallest whole number by which the following number should be multiplied so as to get a perfect square.Also find the square root of the number so obtained.

252

Solution :

Step 1 :

Let us find the prime factors of 252 using the method prime factorization.

Step 2 :

252 = 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 7

Step 3 :