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.
2028
Advertisements
Solution
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
RELATED QUESTIONS
Find the square root of the following number by the prime factorisation method.
9604
Find the smallest number by which the given number must bew multiplied so that the product is a perfect square:
23805
Find the smallest number by which the given number must be divided so that the resulting number is a perfect square:
1800
Find the square root of each of the following by prime factorization.
441
Find the square root the following by prime factorization.
529
Find the square root the following by prime factorization.
8281
Write the prime factorization of the following number and hence find their square root.
7744
Out of 745 students, maximum are to be arranged in the school field for a P.T. display, such that the number of rows is equal to the number of columns. Find the number of rows if 16 students were left out after the arrangement.
Is 90 a perfect square?
_______ is added to 242 to get 252
