Estimate the square root of 24 to the nearest hundredth

9514 1404 393

  √24 ≈ 4.90

Step-by-step explanation:

The square root can be estimated using a linear interpolation between the perfect squares on either side of the number of interest.

  4² = 16

  5² = 25

So, √24 can be estimated to be ...

  (24 -16)/(25 -16) +4 = 8/9 +4 = 44/9 ≈ 4.8888...

This estimate can be refined by doing one iteration of the Babylonian method. That averages the current guess with the value obtained by dividing 24 by that guess.

  √24 ≈ (44/9 +24(9/44))/2 = 4 89/99 ≈ 4.898989...

  √24 ≈ 4.90

A calculator gives the root as approximately 4.89897948557. Rounded to hundredths, that is 4.90.

positive

step-by-step explanation:

the quadrant is facing upwards