Which of the following surds is greatest in magnitude?
sixth root of 17, root 2, twelfth root of 25, cube root of 4

Asked by aahnik.mohanty | 27th Nov, 2017, 08:09: PM

Expert Answer:

begin mathsize 16px style root index 6 of 17 equals 17 to the power of 1 over 6 end exponent equals 17 to the power of 2 over 12 end exponent equals open parentheses 17 squared close parentheses to the power of 1 over 12 end exponent equals open parentheses 289 close parentheses to the power of 1 over 12 end exponent
square root of 2 equals 2 to the power of 1 half end exponent equals 2 to the power of 6 over 12 end exponent equals open parentheses 2 to the power of 6 close parentheses to the power of 1 over 12 end exponent equals open parentheses 64 close parentheses to the power of 1 over 12 end exponent
root index 12 of 25 equals 25 to the power of 1 over 12 end exponent
cube root of 4 equals 4 to the power of 1 third end exponent equals 4 to the power of 4 over 12 end exponent equals open parentheses 4 to the power of 4 close parentheses to the power of 1 over 12 end exponent equals open parentheses 256 close parentheses to the power of 1 over 12 end exponent
rightwards double arrow open parentheses 289 close parentheses to the power of 1 over 12 end exponent less than open parentheses 256 close parentheses to the power of 1 over 12 end exponent less than open parentheses 256 close parentheses to the power of 1 over 12 end exponent less than 25 to the power of 1 over 12 end exponent
rightwards double arrow root index 6 of 17 less than cube root of 4 less than square root of 2 less than root index 12 of 25 end style

Answered by Rashmi Khot | 27th Nov, 2017, 08:44: PM

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