Advertisements
Advertisements
Question
For the following number, find the smallest whole number by which it should be divided so as to get a perfect square number. Also find the square root of the square number so obtained.
2800
Solution
2800 can be factorised as follows.
| 2 | 2800 |
| 2 | 1400 |
| 2 | 700 |
| 2 | 350 |
| 5 | 175 |
| 5 | 35 |
| 7 | 7 |
| 1 |
2800 = 2 × 2 × 2 × 2 × 5 × 5 × 7
Here, prime factor 7 does not have its pair.
If we divide this number by 7, the number will become a perfect square.
Therefore, 2800 has to be divided by 7 to obtain a perfect square.
2800 ÷ 7 = 400 is a perfect square.
400 = 2 × 2 × 2 × 2 × 5 × 5
∴ `sqrt400` = 2 × 2 × 5 = 20
APPEARS IN
RELATED QUESTIONS
For the following number, find the smallest whole number by which it should be divided so as to get a perfect square number. Also find the square root of the square number so obtained.
252
Find the smallest number by which the given number must bew multiplied so that the product is a perfect square:
7688
Write true (T) or false (F) for the following statement.
The number of digits in a square number is even.
Find the square root the following by prime factorization.
1764
A welfare association collected Rs 202500 as donation from the residents. If each paid as many rupees as there were residents, find the number of residents.
Find the least square number, exactly divisible by each one of the numbers:
(i) 6, 9, 15 and 20
By splitting into prime factors, find the square root of 11025.
Examine if the following is a perfect square
725
Find the square root by prime factorisation method
144
