Answer: Option A. -> 382 : A Numbers ending with 2, 3, 7, or 8 at unit's place are never perfect squares. Estimation without actually finding roots: 484 can be the perfect square of a number ending with 2 or 8. 576 can be the perfect square of a number ending with 4 or 6. 529 can be the perfect square of a number ending with 3 or 7.
Question 96. Aman has 729 coins. He gives only a part of these coins to his cousin as his birthday gift. This part is the square root of 729. How many coins did his cousin get?
Answer: Option A. -> 27 : A The square root of 729 should have 3 or 7 in its unit place. Because square of 3 and 7 has 9 in it's units place.Only 27 satisfies this. Thus, Aman's cousin gets 27 coins as a birthday gift. Also, we can find the square root using prime factorization as 729=3×3×3×3×3×3 729=36 Square root of 729 is equal to √729=√36=33=27
Question 97. What will be the number of zeroes in the square of 60?
Answer: Option A. -> 2 : A If a number ends with n zeroes,its square will end with 2n zeroes. Here, 60 ends with one zero, so its square will endwith 2 zeroes. It is important to note thatthis stands true only for natural numbers (not decimals).
Question 98. If A, B, C, ..., X, Y, Z represents digits, which of the following could be a perfect square?
Answer: Option A. -> XX1 : A The numbers 7, 2 and 3 do not appear in the unit place ofany perfect square. So, ABC2 and PQR7 can not be perfect squares and XX1 is the only number which could be a perfect square.
Answer: Option A. -> 1681 : A Perfect squares cannot have 2, 3, 7 or 8in their unit's place. In the given options only 1681 does not endwith a number other than these. The perfect squares of numbers ending in 1 and 9 have 1 at their unit's place. Thus, 1681 could be a perfect square of an integer ending with either 1 or 9.
