Which of the following is a perfect square?

VJesus12 wrote:Which of the following is a perfect square?

A. 649
B. 961
C. 1664
D. 2509
E. 100000

Start with perfect squares that are CLOSE to each answer choice.

A) 649
We know that 25² = 625.
So, perhaps 26² = 649?
NO.
Here's a quick reason why.
25² = (25)(25) = 625
(25)(26) = (25)(25 + 1) = 625 + 25 = 650
So, 26² will be GREATER THAN 650. So 26² CANNOT equal 649

Alternatively, the units digit of 26 is 6, so 26² will have units digit 6 (since 6x6 = 36), but answer choice A has units digit 9
ELIMINATE A

B) 961
We know that 30² = 900.
So, perhaps 31² = 961?
Well, the units digit of 31 is 1, so 31² will have units digit 1. So, we have a definite contender.
Let's check this one.
31² = 961 BINGO!

Answer: B

Cheers,
Brent

VJesus12 wrote:Which of the following is a perfect square?

A. 649
B. 961
C. 1664
D. 2509
E. 100000

The OA is the option B.

How can I determine it without a calculator? Experts, may you give me your help? Thanks.

Let’s look at each answer choice.

A) 649

Since 25^2 = 625, and since 26^2 = 676, we see that 649 is not a perfect square.

B) 961

Since 30^2 = 900 and since 31^2 = 961, we see that 961 is a perfect square.

Answer: B