Advertisements
Advertisements
प्रश्न
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.
2028
उत्तर
2028 can be factorised as follows:
| 2 | 2028 |
| 2 | 1014 |
| 3 | 507 |
| 13 | 169 |
| 13 | 13 |
| 1 |
2028 = 2 × 2 × 3 × 13 × 13
Here, prime factor 3 does not have its pair. If 3 gets a pair, then the number will become a perfect square. Therefore, 2028 has to be multiplied with 3 to obtain a perfect square.
Therefore, 2028 × 3 = 6084 is a perfect square.
2028 × 3 = 6084 = 2 × 2 × 3 × 3 × 13 × 13
∴ `sqrt(6084)` = 2 × 3 × 13 = 78
APPEARS IN
संबंधित प्रश्न
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.
The square of a prime number is prime.
Write true (T) or false (F) for the following statement.
The difference of two square numbers is a square number
Write true (T) or false (F) for the following statement.
The product of two square numbers is a square number.
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 smallest number by which 1152 must be divided so that it becomes a perfect square. Also, find the square root of the number so obtained.
The product of two numbers is 1296. If one number is 16 times the other, find the numbers.
By splitting into prime factors, find the square root of 396900.
Using prime factorisation, find the square roots of 11025
