Question

is 819 a perfect square? show your working​

Answer 1

Question :- is 819 a perfect square ? show your working ?

Solution :-

To check the perfect Square first we will find prime factors of 819.

Prime Factors of 819 :-

→ 819 = 3 * 3 * 7 * 13 = 3² * 7 * 13

Now, as we know that, to be a perfect square all prime factors must be in pairs .(or in power of 2.)

Here as we can see 7 and 13 are not in pairs.

Therefore, we can conclude that, 819 is not a Perfect square.

Note :- [ if in question it has been asked by what number 819 must be multiply to become a perfect square , we need one 7 and one 13 to make pairs of them also. Therefore , we will multiply by (7*13) = 91. }

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Answer 2

819 is not a perfect square

Step-by-step explanation:

The given number is 819

The digit at ones place is 9

We know that 9 is square of 3

Also if 7 is squared we get digit at unit place = 9

Therefore, if 819 is a perfect square of a number then the digit at the unit place of that number must be either 3 or 7

Now the first digit of the number 819 is 8

2² < 8 < 3²

Therefore,

If we take number as 23 then

23² = 529

And 33² = 1089

If the digit at unit place is 7 then

27² = 729

Thus

27² < 819 < 33²

Therefore, 819 is not a perfect square

Hope this answer is helpful.

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