Chapter 4.6, Problem 42HP

To determine

To describe:the difference between an exact value and approximation and give an example of each

Answer to Problem 42HP

The exact value of a square root represent will have infinite non repeating digits and the approximation of a square roota finite number of the digits

Explanation of Solution

Given information:

When finding square roots of numbers that are not perfect squares.

The exact value of a square root of a number is not perfect square. It will be an irrational number. Its answer will be come in decimal which represent will have infinite non repeating digits.

Example $\sqrt{3}=1.7320508$

The approximation of a square root its means rounding the numbers to a certain number of decimal digits it need a finite number of the digits, like $\sqrt{7},\sqrt{\frac{7}{9}}$ etc. Cannot be used in calculation without taking any approximation for these number to use by taking certain approximation up to the desired order of decimal places.

Example $\sqrt{7}=2.645751311$ , $\sqrt{13}=3.605551275$

Hence, the exact value of a square root represent will have infinite non repeating digits and the approximation of a square root a finite number of the digits.