Question

Is \[50\] a perfect square?

Answer 1

Hint: To find whether \[50\] is a perfect square or not, we will perform prime factorisation of \[50\]. Since perfect squares have prime factors, we will try to arrange the factors obtained on prime factorization in pairs of two. If a pair of all prime factors exists then the given number is a perfect square.

Complete step-by-step answer:
A perfect square is a number which is obtained by squaring a whole number. If \[S\] is a perfect square of a whole number \[a\], then \[S\] is the product of \[a\] and \[a\] i.e., \[S = {a^2}\].
This can be also explained in terms of square root. If the square root of a given number is a whole number, then the given number is the perfect square.
Given the number is \[50\], we have to find whether it is a perfect square or not. For this we will use the prime factorization method.
Prime factorization of \[50\]\[ = 2 \times 5 \times 5\]
We can see that 50 has two divisors \[2\] and \[5\], where only \[5\] exists in pairs.
Since, \[2\] does not exist in pairs, therefore \[50\] does not have all its prime factors in pairs.
Hence, \[50\] is not a perfect square.

Note: To find whether the given number is perfect square or not we check that if after prime factorization, when we arrange the factors in pairs, all the elements exist in pairs or not then if exists then is a perfect square. Numbers that have any of the digits \[2\], \[3\], \[7\] or \[8\] in their unit’s place are not perfect squares. Also, note that square of even numbers results in even numbers and square of odd numbers results in odd numbers.