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What is the value of (64516)^(1/2)

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What is the value of (64516)^(1/2)  [#permalink]

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New post 24 Aug 2017, 19:27
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What is the value of \(\sqrt{64516}\)\(\)

A. 256

B. 254

C. 236

D. 234

E. 266

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Re: What is the value of (64516)^(1/2)  [#permalink]

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New post 24 Aug 2017, 20:45
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septwibowo wrote:
fitzpratik wrote:
What is the value of \(\sqrt{64516}\)\(\)

A. 256

B. 254

C. 236

D. 234

E. 266


Solved it with traditional calculation :sad: :sad: :sad:
Does anyone have the more simple approach?


Hi septwibowo
You can use below method -

Realize that the number \(\sqrt{64516}\) is slightly greater than \(62500\).
hence it can be broken as \(= \sqrt{62500+2016} =\) \(\sqrt{(250^{2} + 2016)}\) Now this looks to me of the form \(\sqrt{(a+b)^{2}}\)
so can we break \(2016\) as \(b^2 +2*a*b\). this can be done as \(2016 = 2*250*4 + (4)^2\)
so our number becomes \(= \sqrt{(250 + 4)^2}\)\(= 254\)

Option \(B\)
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Re: What is the value of (64516)^(1/2)  [#permalink]

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New post 24 Aug 2017, 19:35
1
fitzpratik wrote:
What is the value of \(\sqrt{64516}\)\(\)

A. 256

B. 254

C. 236

D. 234

E. 266


Solved it with traditional calculation :sad: :sad: :sad:
Does anyone have the more simple approach?
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Re: What is the value of (64516)^(1/2)  [#permalink]

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New post 25 Aug 2017, 06:20
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septwibowo I would do process elimination.
Only B works out to square root of 64516.
Proof 254 x 254 = 64516
Hope this helps.
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Re: What is the value of (64516)^(1/2)  [#permalink]

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New post 25 Aug 2017, 09:23
4
septwibowo wrote:
fitzpratik wrote:
What is the value of \(\sqrt{64516}\)\(\)

A. 256

B. 254

C. 236

D. 234

E. 266


Solved it with traditional calculation :sad: :sad: :sad:
Does anyone have the more simple approach?

Hi septwibowo

One thing to notice here is that 625 is 25*25
so, 62500 will be 250*250, so our answer is greater than 250, which rules out C and D,

now numbers left are 254, 256 and 266. I start with 256 i get 256*256 = 65536, Now since 65536 > 64516, answer is 254 or B!
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Re: What is the value of (64516)^(1/2)  [#permalink]

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New post 25 Aug 2017, 09:28
1
fitzpratik wrote:
septwibowo wrote:
fitzpratik wrote:
What is the value of \(\sqrt{64516}\)\(\)

A. 256

B. 254

C. 236

D. 234

E. 266


Solved it with traditional calculation :sad: :sad: :sad:
Does anyone have the more simple approach?

Hi septwibowo

One thing to notice here is that 625 is 25*25
so, 62500 will be 250*250, so our answer is greater than 250, which rules out C and D,

now numbers left are 254, 256 and 266. I start with 256 i get 256*256 = 65536, Now since 65536 > 64516, answer is 254 or B!


Thanks fitzpratik , this is exactly what I did :grin: :grin:

We can also use niks18 approach, kudos for all of you guys!
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Re: What is the value of (64516)^(1/2)  [#permalink]

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New post 12 Oct 2017, 06:36
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
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What is the value of (64516)^(1/2)  [#permalink]

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New post 12 Oct 2017, 10:03
2
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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Re: What is the value of (64516)^(1/2)  [#permalink]

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New post 12 Oct 2017, 12:08
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I think that it is also helpful to realize that it 64516 is divisible by 4 because the last 2 digits (16) are divisible by 4. To find out if it's divisible by 6, it has to be even and the sum of all the digits must be divisible by 3. It is even, but 6+4+5+1+6 = 22 which is not divisible by 3. This rules out all but B and D. Then using the 250^2 as mentioned already, you can rule out D, or you can just start multiplying the last two digits of B and D to use trial by elimination.
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What is the value of (64516)^(1/2)  [#permalink]

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New post 12 Oct 2017, 12:19
1
zflodeen wrote:
I think that it is also helpful to realize that it 64516 is divisible by 4 because the last 2 digits (16) are divisible by 4. To find out if it's divisible by 6, it has to be even and the sum of all the digits must be divisible by 3. It is even, but 6+4+5+1+6 = 22 which is not divisible by 3. This rules out all but B and D. Then using the 250^2 as mentioned already, you can rule out D, or you can just start multiplying the last two digits of B and D to use trial by elimination.

zflodeen -- Gah! I was so focused on unpredictable squares that I did not even think about divisibility rule for 6. That'll teach me.

That's the best shortcut, IMO. Kudos.
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Re: What is the value of (64516)^(1/2)  [#permalink]

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New post 06 Dec 2017, 21:18
Here's the method I used which saved a lot time for me.

Start off by rewriting using the answer choices one by one, and removing the hundred's place digit.

A. 56

B. 54

C. 36

D. 34

E. 66

We have to pick the number which yields 16 at the end when squared.

Go for A.

56
*56
---------
XX36
XX00
----------

What I did here was, I didn't calculate the entire thing because I know that the last two digits have to be 16. Here, the last two digits are 36, so eliminate the answer choice.

Go for B.

54
*54
---------
XX16
XX00
----------

The last two digits here is 16, so hold onto the answer choice and repeat the same with C,D,E. The reason we repeat the method is that, C,D,E might also yield 16 at the end. In such cases, we have to do the entire calculation instead of just the last two digits like I did.

Fortunately, none of the other options yielded 16 at the end apart from Option B, so we are good. B is the answer. Hope my explanation helps!
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