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(496)^(1/4) is between

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jlgdr
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(496)^(1/4) is between [#permalink] New post   17 Sep 2013, 17:28
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\(\sqrt[4]{496}\) is between

(A) 3 and 4
(B) 4 and 5
(C) 5 and 6
(D) 6 and 7
(E) 7 and 8
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B
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Re: (496)^(1/4) is between [#permalink] New post   17 Sep 2013, 19:00
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jlgdr wrote:
4th root of 496 is between

(A) 3 and 4
(B) 4 and 5
(C) 5 and 6
(D) 6 and 7
(E) 7 and 8


4^4 = 2^8 = 256;
5^4 = 625;

\(4^4 < 496 < 5^4\) --> \(4<\sqrt[4]{496}<5\).

Answer: B.
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Re: (496)^(1/4) is between [#permalink] New post   18 Feb 2017, 07:47
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jlgdr wrote:
4th root of 496 is between

(A) 3 and 4
(B) 4 and 5
(C) 5 and 6
(D) 6 and 7
(E) 7 and 8


\(\sqrt{496} = 22.xx\)

\(\sqrt{22.xx} = 4.xx\)

Thus, the 4th root of 496 is between 4 and 5

Answer will be (B) between 4 and 5
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Re: (496)^(1/4) is between [#permalink] New post   26 Sep 2020, 17:17
16 square is 256 and 25 sqaure is 625 , so 496 must lie between 4 and 5 since it is a 4th square root.
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Re: (496)^(1/4) is between [#permalink] New post   18 Jan 2021, 11:23
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jlgdr wrote:
4th root of 496 is between

(A) 3 and 4
(B) 4 and 5
(C) 5 and 6
(D) 6 and 7
(E) 7 and 8


\(4^4 = 256\), so the 4th root of 256 equals 4
\(5^4 = 625\), so the 4th root of 625 equals 5

Since 496 lies BETWEEN 256 and 625, the fourth root of 496 must be between 4 and 5

Answer: B
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Re: (496)^(1/4) is between [#permalink] New post   12 Mar 2024, 09:02
 
jlgdr wrote:
\(\sqrt[4]{496}\) is between

(A) 3 and 4
(B) 4 and 5
(C) 5 and 6
(D) 6 and 7
(E) 7 and 8

­Alternate approach using options , 

(A) 3^4 to 4^4 = 81 to 256 not possible as the no is 496 which is outside range
(B) 4^4 to 5^4 = 256 to 625 Possible.
(C) 5^4 and 6^4 = 625 to 1296 not possible as the no is 496 which is outside range
(D) 6^4 and 7^4 = 1296 to .......... not possible as the no is 496 which is outside range
(E) 7^4 and 7^4 = 2401 to .......... not possible as the no is 496 which is outside range

Answer must be (B)
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Re: (496)^(1/4) is between [#permalink]
12 Mar 2024, 09:02
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