Question

Using the ratio of perfect squares method, what is square root of 14 rounded to the nearest hundredth? Do not use your calculator to answer this question. Use the ratio of perfect squares method.

Answer 1

The square root of 14 rounded to the nearest hundredth without using the calculator can be done this way. Follow these steps:
1. Guess
2. Divide
3. Average

GUESS.
1. Make good guess. We'll just use 2

DIVIDE.
2. Divide 14 by our guess of 2 = 7.

AVERAGE.
3. Average 7 and 2: (7+2)/2 = 4.5

Here, we repeat step 2 using 7 as our new guess, 4.5
2. 14/4.5 = 3.1
3. (3.1 + 4.5)/2 = 3.8

2. 14/3.8 = 3.7
3. (3.7 + 3.3)/2 = 3.5

2. 14/3.5 = 4
3. (3.5 + 4)/2 = 3.75

2. 14/3.75 = 3.7
3. (3.75 + 3.7)/2 = 3.725

so on and so forth until the pattern remains in 3.7