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.
1458
Advertisements
Solution
1458 can be factorised as follows:
| 2 | 1458 |
| 3 | 729 |
| 3 | 243 |
| 3 | 81 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
1458 = 2 × 3 × 3 × 3 × 3 × 3 × 3
Here, prime factor 2 does not have its pair. If 2 gets a pair, then the number will become a perfect square. Therefore, 1458 has to be multiplied with 2 to obtain a perfect square.
Therefore, 1458 × 2 = 2916 is a perfect square.
1458 × 2 = 2916 = 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3
∴ `sqrt(2916)` = 2 × 3 × 3 × 3 = 54
APPEARS IN
RELATED QUESTIONS
For the following number, find the smallest whole number by which it should be divided so as to get a perfect square number. Also find the square root of the square number so obtained.
2800
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 be divided so that the resulting number is a perfect square:
1800
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.
No square number is negative.
Find the smallest number by which 180 must be multiplied so that it becomes a perfect square. Also, find the square root of the perfect square so obtained.
The area of a square field is 5184 cm2. A rectangular field, whose length is twice its breadth has its perimeter equal to the perimeter of the square field. Find the area of the rectangular field.
By splitting into prime factors, find the square root of 11025.
Find the square root of 6400.
Using prime factorisation, find which of the following are perfect squares.
11250
