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(496)^(1/4) is between

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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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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

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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