Question

1. Use the Babylonian method for your next estimate for the square root of 130 by using 11.4022 as your guess. What is your result?
a) 11.4018
b) 11.3043
c) 11.6102
d) 16.1246

2. Naila wants to use the Babylonian method to estimate the square root of 58 to the neatest hundredth. Her initial estimate is 7.8. What is her estimate after she correctly completes the Babylonian method once?
a) 7.43
b) 7.44
c) 7.61
d) 7.62

3. Use the Babylonian method for your next estimate of the square root of 115 by using 10.7262 as your guess. What is your result?
a) 10.7238
b) 10.6107
c) 10.8393
d) 16.0869

4. Kayla wants to use the Babylonian method to estimate the square root of 43 to the nearest hundredth. Her initial estimate is 6.9. What is her estimate after she correctly completes the Babylonian method once?
a) 6.44
b) 6.57
c) 6.45
d) 6.56

PLEASE HELP FAST NEED THE ANSWERS ASAP

Answer 1

#1 - a) 11.4018
#2 - d) 7.62
#3 - a) 10.7238
#4 - b) 6.57

Explanation
#1 - The initial guess is 11.4022.  We first divide 130 by this guess:
130÷11.4022 = 11.40130852

We now average this number with the initial guess:
(11.40130852 + 11.4022)/2 ≈ 11.4018

#2 - The initial guess is 7.8.  We divide 58 by this guess:
58÷7.8 = 7.435897436

We now average this number with the initial guess:
(7.435897436 + 7.8)/2 = 7.617948718 ≈ 7.62

#3 - The initial guess is 10.7262.  We divide 115 by this guess:
115÷10.7262 = 10.72141112

We now average this number with the initial guess:
(10.72141112 + 10.7262)/2 = 10.72380556 ≈ 10.7238

#4 - The initial guess is 6.9.  We divide 43 by this guess:
43÷6.9 = 6.231884058

We now average this number with the initial guess:
(6.231884058+6.9)/2 = 6.565942029 ≈ 6.57