Chapter 1.3, Problem 2P

To determine

To find: the value of $\sqrt{34}$ to the nearest value of integer.

Answer to Problem 2P

The nearest value of integer is $6$ .

Explanation of Solution

Given:

  $\sqrt{34}$ .

Concept used:

The sets of integers are:

  $z=\left\{\mathrm{.....},-3,-2,-1,0,1,2,3,\mathrm{.....}\right\}$ .

The fraction or decimal which are not further divisible are not include in integers.

The nearest integer can be measure by taking round off of the decimal or fraction value.

  $\begin{array}{l}0.2\approx 0.\\ 3.8\approx 4.\end{array}$

Check the first value after decimal point if it is less than $5$ then take the preceding number if the value after decimal is more than $5$ then add one more to the preceding number.

Calculation:

Square root of $34$ can be calculate using the calculator it will be in decimal form since, it is not the perfect square.

  $\sqrt{34}=5.8309518948453$ .

Nearest tenth digit round off:

  $\sqrt{34}\approx 5.8$ .

Nearest $100th$ digit round off:

  $\sqrt{34}\approx 5.83$ .

Nearest $1000th$ digit round off:

  $\sqrt{34}\approx 5.831$ .

Since, the square root of $34$ is an irrational number, it cannot make it into an exact fraction. However, it can make it into an approximate fraction using the square root of $34$ rounded to the nearest hundredth.

  $\begin{array}{l}\sqrt{34}.\\ \Rightarrow \frac{5.83}{1}=\frac{583}{100}.\end{array}$

Hence, the nearest value of integer is $6$ .