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.
1008
Solution
1008 can be factorised as follows:
| 2 | 1008 |
| 2 | 504 |
| 2 | 252 |
| 2 | 126 |
| 3 | 63 |
| 3 | 21 |
| 7 | 7 |
| 1 |
1008 = 2 × 2 × 2 × 2 × 3 × 3 × 7
Here, prime factor 7 does not have its pair. If 7 gets a pair, then the number will become a perfect square. Therefore, 1008 can be multiplied with 7 to obtain a perfect square.
1008 × 7 = 7056 = 2 × 2 × 2 × 2 × 3 × 3 × 7 × 7
Therefore, 1008 × 7 = 7056 is a perfect square.
∴ `sqrt(7056)` = 2 × 2 × 3 × 7 = 84
APPEARS IN
RELATED QUESTIONS
Find the square root of the following number by the prime factorisation method.
4096
Find the square root of the following number by the prime factorisation method.
529
Find the smallest square number that is divisible by each of the numbers 4, 9, and 10.
Find the smallest number by which the given number must bew multiplied so that the product is a perfect square:
12150
By just examining the unit digit, can you tell which of the following cannot be whole square?
1024
Write true (T) or false (F) for the following statement.
There are fourteen square number upto 200.
Find the square root of each of the following by prime factorization.
441
Find the square root the following by prime factorization.
196
Find the square root the following by prime factorization.
586756
Examine if the following is a perfect square
190
