Question

Name the subset(s) of real numbers to which each number belongs. Then order the numbers from least to greatest. 105−−−√,−4,43

Answer 1

Answer:

(a)

$\sqrt{105} => Irrational$

$-4 => Integer$

$\frac{4}{3} => Rational$

(b)

$-4$    $\frac{4}{3}$     $\sqrt{105}$

Step-by-step explanation:

Given

$\sqrt{105}$

$-4$

$\frac{4}{3}$

Solving (a): The category of number the belong to

$\sqrt{105}$

Solve the square root

$\sqrt{105} = 10.246950766$

The result is irrational;

So:

$\sqrt{105} => Irrational$

$-4 => Integer$

$\frac{4}{3}$

This has an integer numerator and denominator;

So:

$\frac{4}{3} => Rational$

Solving (b): Order from least to greatest

i. $\sqrt{105} = 10.246950766$

ii. $-4$

iii. $\frac{4}{3} = 1.33333$

List out the corresponding numbers:

10.246950766; -4 and 1.333333

Reorder: from least to greatest:

-4; -1.3333333 and 10.246950766

Hence; The correct order is:

$-4$    $\frac{4}{3}$     $\sqrt{105}$