Multiple choice

The approximate value of $\sqrt [ 5 ]{ 33 } $ correct to $4$ decimal places is

  1. $2.0000$
  2. $2.1001$
  3. $2.0125$
  4. $2.0500$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

33^(1/5) is slightly more than 32^(1/5) = 2. Using linear approximation: f(x+dx) = f(x) + f'(x)dx. f(32) = 2, f'(x) = (1/5)x^(-4/5), f'(32) = (1/5)(1/16) = 1/80 = 0.0125. So 33^(1/5) approx 2 + 0.0125 = 2.0125.

AI explanation

Using the approximation formula for roots, (32 + x)^(1/5) is approximately equal to the fifth root of 32 plus x divided by 5 times the fifth root of 32 to the fourth power. The fifth root of 32 is 2, and 2 to the fourth power is 16, making the denominator 80. For the number 33, x is 1, so we calculate 2 plus 1/80, which equals 2 plus 0.0125, resulting in 2.0125.

Keep practicing — related questions