Question

find the greatest number of 6 digits which is a perfect square. Find the square root of this number.

Answer 1

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Answer 2

To find: The greatest 6 digits number which is a perfect square and square root of that number.

Solution:

We know that 999999 is the largest 6 digits number but it's not a perfect square. So, we need to find a number less than 999999 which is a perfect square.

Steps to find the greatest 6 digits perfect square number:

Step 1 : Use the long division method to find the square root of 999999.

  Steps to find the square root using the long division method:

• Group the digits in pairs, starting with the unit place digits called periods. If any digit is left unpaired, it will be considered a different period.        
• Consider the largest number whose square is equal to or just less than the first period. Take that number as the divisor and also as the quotient.
• Subtract the product of divisor and quotient from the first period and bring down the next period to the right of the remainder. This becomes the new dividend.
• The new divisor is obtained by taking two times the quotient and annexing with it a suitable digit which is also taken as the next digit of the quotient, chosen in such a way that the product of the new divisor and the digit is equal to or just less than the new dividend.
• Repeat the above steps till all the periods have been taken up. The quotient obtained is the required square root of the given number and the remainder obtained (if any) is the number, which when subtracted from the given number, the number will become a perfect square.

Using the above steps to find the square root of 999999, we get

Quotient = 999

Remainder = 1998

Step 2 : Subtract the remainder from 999999.

i.e., 999999 - 1998 = 998001

Now, using the prime factorization method, 998001 can be expressed as:

998001 = 3 × 3 × 3 × 3 × 3 × 3 × 37 × 37

Square root of 998001 = 3 × 3 × 3 × 37 = 999

Hence, the greatest 6 digits number which is a perfect square is 998001 and its square root is 999.