Chapter A.1, Problem 6E

Solution

Find the indicated real roots. Cube root of $\frac{-27}{8}$ .

  $\frac{-3}{2}$ .

Given:

The given no. is $\frac{-27}{8}$ .

Concept Used:

• Root, in mathematics, a solution to an equation, usually expressed as a number or an algebraic formula.

Calculation:

The given number is $\frac{-27}{8}$ .

Cube root of $\frac{-27}{8}$ is:

Let $x^3=\frac{-27}{8}$

  $\begin{array}{l}x=\sqrt[3]{\frac{-27}{8}}\\ $ x={(\frac{-27}{8})}^{1/3}$x={\left(\frac{(-3)\cdot (-3)\cdot (-3)}{2\cdot 2\cdot 2}\right)}^{1/3}\\ x={\left(\frac{{(-3)}^3}{2^3}\right)}^{1/3}\\ x=\frac{{\left({(-3)}^3\right)}^{1/3}}{{(2^3)}^{1/3}}\\ x=\frac{-3}{2}\end{array}$

Thus the cube root of $\frac{-27}{8}$ is $\frac{-3}{2}$ .