Question

Four students provide the following approximations for StartRoot 0.89 EndRoot. Anyah states that StartRoot 0.89 EndRoot is between 0.44 and 0.45 because 0.44 less-than StartFraction 0.89 Over 2 EndFraction less-than 0.45. Matthew states that StartRoot 0.89 EndRoot is between 0 and 1 because 0 less-than 0.89 less-than 1. Rhoda states that StartRoot 0.89 EndRoot is between 0.9 and 1.0 because 0.9 squared less-than 0.89 less-than 1.0 squared. Ming states that StartRoot 0.89 EndRoot is between 0.93 and 0.95 because (0.93) squared less-than 0.89 less-than (0.95) squared. Which solution(s) are correct?

Answer 1

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Four students provide the following approximations for StartRoot 0.89 EndRoot. Anyah states that StartRoot 0.89 EndRoot is between 0.44 and 0.45 because 0.44 less-than StartFraction 0.89 Over 2 EndFraction less-than 0.45. Matthew states that StartRoot 0.89 EndRoot is between 0 and 1 because 0 less-than 0.89 less-than 1. Rhoda states that StartRoot 0.89 EndRoot is between 0.9 and 1.0 because 0.9 squared less-than 0.89 less-than 1.0 squared. Ming states that StartRoot 0.89 EndRoot is between 0.93 and 0.95 because (0.93) squared less-than 0.89 less-than (0.95) squared. Which solution(s) are correct?

Answer 2

Given :  Four students provide the following approximations for  √0.89  

Anyah states that √0.89    is between 0.44 and 0.45 because 0.44 < 0.89 /2  < 0.45

Matthew states that √0.89   is between 0 and 1 because 0 < 0.89 < 1

Rhoda states that √0.89   is between 0.9 and 1.0 because  0.9² < 0.89 <  1²

Ming states that √0.89   is between 0.93 and 0.95 because  0.93² < 0.89 <  0.95²

To find : Which solution(s) are correct?

Solution:

Anyah states that √0.89    is between 0.44 and 0.45 because 0.44 < 0.89 /2  < 0.45

This is Incorrect

Matthew states that √0.89   is between 0 and 1 because 0 < 0.89 < 1

This is not approximation but too wide range

Rhoda states that √0.89   is between 0.9 and 1.0 because  0.9² < 0.89 <  1²

This is correct

Ming states that √0.89   is between 0.93 and 0.95 because  0.93² < 0.89 <  0.95²

This is also correct

Rhoda and Ming both are correct  but Ming has closer approximation because of the result upto two decimal points

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