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.
180
Solution
180 can be factorised as follows:
| 2 | 180 |
| 2 | 90 |
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
180 = 2 × 2 × 3 × 3 × 5
Here, prime factor 5 does not have its pair. If 5 gets a pair, then the number will become a perfect square. Therefore, 180 has to be multiplied with 5 to obtain a perfect square.
180 × 5 = 900 = 2 × 2 × 3 × 3 × 5 × 5
Therefore, 180 × 5 = 900 is a perfect square.
∴ `sqrt(900)` = 2 × 3 × 5 = 30.
APPEARS IN
RELATED QUESTIONS
Find the square root of the following number by the prime factorisation method.
9216
Find the smallest square number that is divisible by each of the numbers 4, 9, and 10.
Write five numbers which you cannot decide whether they are square just by looking at the unit's digit.
Find the smallest number by which 147 must be multiplied so that it becomes a perfect square. Also, find the square root of the number so obtained.
Write the prime factorization of the following number and hence find their square root.
7744
By splitting into prime factors, find the square root of 194481.
Find the square root of 6400.
Is 90 a perfect square?
Find the square root by prime factorisation method
144
Find the smallest square number divisible by each one of the numbers 8, 9 and 10.
