Question

Find the greatest number of two digits which is a perfect square.

Answer 1

Hint: We need to find the greatest number of two digits which is a perfect square so we will first find the greatest two-digit number and see whether it is a perfect square or not. If not, then we will use the division algorithm and find the remainder so, if we add the remainder into the 2-digit greatest number it results in a 3-digit number, so we will subtract the remainder from the 2-digit number to find the greatest number which is a perfect square.

Complete step-by-step answer:
The aim is to find the greatest number of two digits which is a perfect square.
As we know that 9 is the greatest digit of all the digits so we will form a 2-digit number.
Hence, 99 is the greatest two-digit number.
Now, we can see that 99 is not a perfect square so, we will use the division algorithm to find the remainder.
Thus, division algorithm states that \[divisor = dividend\left( {quotient} \right) + remainder\]
This gives us \[99 = 9\left( 9 \right) + 18\]
Hence, we got the remainder as 18. Thus, now, to find the perfect subtract, either we need to add 18 or subtract 18 from 99.
If we will add 18 and form a perfect square, it will lead to a 3-digit number. Thus, we will subtract 18 from the number.
Hence, we get,
\[ \Rightarrow 99 - 18 = 81\]
Thus, we get that 81 is the greatest number of two digits which is a perfect square.

Note: To form a greatest 2-digit number, we have formed a number of the greatest digit 9. Next, we have checked whether 99 is a perfect square or not. As 99 is not a perfect square we can divide 99 by 9 to find the remainder and subtract it from 99 to find a perfect square.