Question

Find the largest number of six – digits which is a perfect square.

Answer 1

Hint:We will solve this question using the long division method. The student must know the long division method very thoroughly. The division method is stated in the solution thoroughly and is applicable to any digit number.

Complete step by step answer:
We know that the largest six – digit number is 999999. But, this is not a perfect square. Therefore, we need to find the largest six – digit number that is a perfect square, and we will find this using the long division method, as mentioned in the hint above.
So firstly, we will take the largest six – digit number, i.e. 999999 and place bars on every pair of digits such as:-

Now, we are going to solve this using the long division method:-

Now as we can see that there is a remainder left, i.e. 1998. So, we are going to subtract 1998 from the biggest six – digit number, i.e. 999999. The difference that we will get is 998001.
Therefore, the answer for this question is 998001.
998001 is the largest six – digit number that is a perfect square. It is the square of 999, which means, \[{{\left( 999 \right)}^{2}}\] = 998001.

Note:To solve this question, one must know the long division method properly, because, if any mistake is done, then the answer so obtained will be wrong. An example is given below; you can refer to the example given below.
Let us take any number. Say, 390625. You can find the square root of this number by the following method.

So, the answer obtained is 625.
Which means that (625 x 625) will be 390625, i.e., \[{{\left( 625 \right)}^{2}}\] is equal to 390625.