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
Advertisements
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.
1764
Find the smallest square number that is divisible by each of the numbers 8, 15, and 20.
Write five numbers which you cannot decide whether they are square just by looking at the unit's digit.
Write true (T) or false (F) for the following statement.
No square number is negative.
Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication:
25
Find the square root the following by prime factorization.
1156
By splitting into prime factors, find the square root of 396900.
Find the square root of 6400.
Examine if the following is a perfect square
725
A square board has an area of 144 square units. How long is each side of the board?
