(496)^(1/4) is between

Question

\sqrt {496}  is between
 
 (A) 3 and 4
 (B) 4 and 5
 (C) 5 and 6
 (D) 6 and 7
 (E) 7 and 8

Bunuel · Accepted Answer

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

4^4 < 496 < 5^4  -->  4<\sqrt {496}<5 .

Answer: B.

Abhishek009 · Answer

\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

gmatnerdforever · Answer

16 square is 256 and 25 sqaure is 625 , so 496 must lie between 4 and 5 since it is a 4th square root.

BrentGMATPrepNow · Answer

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

Abhishek009 · Answer

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)

quamminus · Answer

How do we know that we are looking for the roots here?

Bunuel · Answer

\sqrt {496}  means 4th root of 496.

(496)^(1/4) is between

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(496)^(1/4) is between

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