JannikHeine wrote:
fitzpratik wrote:
What is the value of \(\sqrt{64516}\)\(\)
A. 256
B. 254
C. 236
D. 234
E. 266
Can´t you just simply recognize that 4x4 is 16 which rules out every answer choice that ends with something different than 6. Than apply the logic used above
JannikHeine , I can see how it would seem logical to think that way.
The answer is:
No. (6 * 6) also ends in 6. This is multiplication. We don't know what those extra digits are going to do when multiplied by each other.
There are 2- 3- and x-digit numbers ending in 6 whose square ends in 16.
For example
246 * 246 = 60516
196 * 196 = 38416
46 * 46 = 2116
You can use shortcuts that aren't terribly difficult. I multiplied the first two digits of each answer and compared the 3-digit result with the first three digits of the prompt, i.e., 65416 --> 654xx
I knew that 25 * 25 = 625. (If not, multiply.) 625 is pretty close to 654. 25_ was still in.
Like
fitzpratik : C and D, with first two digits of 23, were out.
If 25_\(^2\) = 625xx isn't quite 654xx, 23_\(^2\) would certainly not be closer.
(Proof: 23 * 23 = 529, so 23_\(^2\) would not even make it into the 60,000s.)
Then E: (26*26) = 676. Too large. Eliminate
Down to A and B. You only have to calculate one. I used B:
254 * 254 = 65416
But if I had chosen A:
256 * 256 = 65536. Too large. The right choice must be
Answer B
Hope it helps.
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