Question

Find the least number which must be subtracted from 1989 so as to get a perfect
square. Also find the square root of the perfect square so obtained.​

Answer 1

Answer:

Hope this helps you ??

Step-by-step explanation:

Here we are going to see how to find the least number to be  the given number to get a perfect square.

For this, we use the method called long division.

Let us see an example to understand the concept.

Example 1 :

Find the least number which must be subtracted from 1989 so as to get a perfect square

Solution :

Step 1 :

Separate the digits by taking commas from right to left once in two digits.

19, 89

When we do so, we get 19 before the comma.

Step 2 :

Now we have to multiply a number by itself such that the product ≤ 4

(The product must be greatest and also less than 19)

The above condition will be met by “4”.

Because 4 ⋅ 4  =  16

Now this situation is explained using long division

In the above picture, 16 is subtracted from 19 and we got the remainder 3.

Step 3 :

Now, we have to bring down 89 and quotient 4 to be multiplied by 2. So we get 8.

By multiplying 4 and 84 we get 336.

If we subtract 336 from 389, we get 53.

We don't have to continue hereafter.

44 (44)  =  1936

If we subtract 53 from 1989, we get 1936 which is the perfect square.

Hence 53 is the least number to be subtracted from the given number (1989) to get a perfect square.