Question

If the digit in the units place of a square natural number is 6, then the digit in the tens place will be:

Answer 1

It will be 4as if we do the square of 8then it will be 64 where 6is at unit place and 4is at tens place

Answer 2

The digit at the tens place can be 1, 3, 5, 7, or 9.

• For a number to have a units digit of a square of a natural number as 6. The natural numbers should have the unit digit either 4, or 6. Because The even powers of 4 in 4^n have units digit 6. For any powers of 6 in 6^n, the units digit is 6.

• Consider the following examples,

=> 4² = 16, 6² = 36, 14² = 196, 16² = 256, 24² = 576, 26² =676, 34² = 1156, 36² = 1296.

• From the above examples, it can be observed that the tens digit of any powers with units digit 4 is ending with 1, 3, 5, 7, or 9.
• The is no possibility for the occurrence of even numbers in the tens digit as shown above.

Hence, the possible digits in the tens place are 1, 3, 5, 7, or 9.