Solving square root word problem[Step-by-step]

In this post, you will learn to solve the square root word problems using the long division method. You can use other methods as well, but in this post, we will solve them by the long division method.

Q.1 Find the smallest number which when added to 6156 makes it a perfect square.


Method : 1 

Perfect square: A number whose square root is a whole number (Neither decimal nor fraction) is called a perfect square.

Step:01 Find the square root of the given number 

Square root word problem

As you can see, we get 72 as the remainder. It indicates,6156 is not a perfect square 

Step:02 Find the nearest possible perfect square 

But, How? Well to figure out this, you should start with the Quotient of the division 

Solving square root word problem

In the above division, we have 78.[Something] as quotient. It shows 

6156 > 78²                     [78²= 6084]

So, the nearest possible perfect square is 79² i.e 6241

Now, we have to find a number which when added to 6156 make it erfect square of 79.

Required number = 6241 – 6156 

  = 85 

Therefore, 85 is the smallest number which when added to 6156 makes it a perfect square 


Step: 01 Use the same long division process 

Step: 02 

Solving square root word problem

At this stage, for blank boxes, think of the number whose product is greater than 1256.Try to put different values and check the result 

The required answer is 9 . How? See the image 

Solving word problem of square root

Product: 149 × 9= 1341 which is greater than 1256. That’s why the remainder is negative 

∴ 85 is the smallest number which when added to 6156 makes it a perfect square. Yes, it is our result [Check first method answer] both answers are the same.

Q.2 What must be subtracted from 1394 to obtain a perfect square? What is the perfect square so obtained? write its square root 


Step: 01 Try to find square root using the long division method 

Solving square root

So, we get 25 as the remainder.

For perfect square, 25 should be subtracted from 1394 [To make this extra remainder 0]

1394 – 25= 1369 

Now, 1369 is a perfect square whose square root is 37.

Square root of 1369

Q.3 Find the smallest 6-digit number ,which is a perfect square 


We know , 

Smallest 6-digit number is 10,00 ,00

Now ,we have to find the smallest 6-digit number which is perfect square .

Using long division method ,

Smallest 6-digit perfect square

We get 489 as remainder 

So, required perfect square = 100000+489 = 100489 

Q.4 Find the largest 4-digit number ,which is a perfect square 


We know,

Largest 4-digit number = 9999

Using long division method ,

Square root of 4-digit largest number

We get 198 as remainder 

∴ 198 should be subtracted from 9999 to obtain a perfect square 

9999 – 198 = 9801 

Square root of 9801 is 99 

Square root of 9801

Conclusion : 

  • The smallest type numbers like a 4-digit smallest perfect square,6-digit smallest perfect square, etc, we add the remainder in the given number to make it a perfect square.
  • And largest type problems like a 4-digit largest perfect square,6 digits largest perfect square, etc, we subtract the remainder from a given number to make it a perfect square.

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