Advertisements
Advertisements
Question
For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.
180
Advertisements
Solution
180 can be factorised as follows:
| 2 | 180 |
| 2 | 90 |
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
180 = 2 × 2 × 3 × 3 × 5
Here, prime factor 5 does not have its pair. If 5 gets a pair, then the number will become a perfect square. Therefore, 180 has to be multiplied with 5 to obtain a perfect square.
180 × 5 = 900 = 2 × 2 × 3 × 3 × 5 × 5
Therefore, 180 × 5 = 900 is a perfect square.
∴ `sqrt(900)` = 2 × 3 × 5 = 30.
APPEARS IN
RELATED QUESTIONS
For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.
768
Write true (T) or false (F) for the following statement.
The square of a prime number is prime.
Find the square root of each of the following by prime factorization.
441
Find the square root the following by prime factorization.
3013696
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.
A society collected Rs 92.16. Each member collected as many paise as there were members. How many members were there and how much did each contribute?
Find the square root by prime factorisation method
144
Find the square root by prime factorisation method
256
Find the cube root of 729 and 6859 prime factorisation
Using prime factorisation, find which of the following are perfect squares.
484
