Question

By what number should 4246 be subtracted to make it a perfect square. Also find the square root of the number so obtained.

Answer 1

Answer:

need to find the least number after subtracting which the resulting number is a perfect square.

Clearly, (80)² > 6252 > (78)² ; one can see obviously that 6400 which is square of 80 is more than 6252, which in turn is more than square of 75 i.e. 5625.

Now square of 79 = 79×79 = 6241

So least number required = 6252 - 6241 = 11.

The square root of 6241 = 79.

You can also find the square root of 6252 first by long root method. You will get it as 79 with some decimal part. So, the nearest perfect square will be of 79.

Explanation:

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Answer 2

Explanation:

We have,

1989 be make perfect square.

We know that,

44

2

=1936<1989

45

2

=2025>1989

Let x be added or subtracted in 1989

Then,

x+44

2

=1989

⇒x+1936=1989

⇒x=1989−1936

⇒x=53

53 is subtracted from 1989 making perfect square.

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