Find the least number by which 1800 should be multiplied so that it becomes a perfect Square. Also find the square root of the perfect square thus obtained
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 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 :
‘7’ remains without a pair.
Hence, 252 must be multiplied by 7 to make it a perfect square.
√(252 ⋅ 7) = √(2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 7 ⋅ 7)
√1764 = 2 ⋅ 3 ⋅ 7 = 42
Example 3 :
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.
180
Solution :

Step 1 :
Let us find the prime factors of 180 using the method prime factorization.
Step 2 :
180 = 2 ⋅ 2 ⋅ 5 ⋅ 3 ⋅ 3
Step 3 :
‘5’ remains without a pair.
Hence, 180 must be multiplied by 5 to make it a perfect square.
Answer:
it should be multiplied by 2 to get a perfect square
Step-by-step explanation:
by doing so you get 3600
and it's square root is 60