Question

What least number must be subtracted from 433026 to get a perfect square?

Answer 1

Question :- What least number must be subtracted from 433026 to get a perfect square ?

Solution :-

To find the number first we have to find the Perfect square near to 433026 .

Lets Try to solve with some trick :-

→ Last two digits have 6 in Last = So, if it is a perfect Square , than we have 4 or 6 in Last . (4² = 16, 6² = 36).

Now,

→ Remaining digits are = 4330

So,

→ upto 4330 we can go to Square of = 65 that is 4225 .

Than,

→ 433026 will either perfect square of 654 or 656 .

So,

→ (654)² = 427716

→ (656)² = 430336

Therefore, we can say that,

→ Square of 656 is the Nearest Perfect Square Number . {As (657)² > 430336.}

Hence,

→ Least number must be subtracted from 433026 to get a perfect square = 433026 - 430336 = 2690 .(Ans.)

{ Note :- Also the Perfect square number is square of 256.}

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