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Chapter 10: Problem 2

How do you eliminate the radical from an equation like \(\sqrt[3]{x}=2 ?\)

Short Answer

Expert verified
To eliminate the radical from the equation \(\sqrt[3]{x} = 2\), raise both sides of the equation to the power of 3: \((\sqrt[3]{x})^3 = (2)^3\). Simplifying the equation results in \(x = 8\).

Step by step solution

01

Identify the radical to be eliminated

We want to eliminate the cube root \(\sqrt[3]{x}\) from the equation \(\sqrt[3]{x} = 2\), so we will focus on this term.
02

Raise both sides of the equation to the power of 3

To eliminate the cube root, we will raise both sides of the equation to the power of 3. This can be represented as \((\sqrt[3]{x})^3 = (2)^3\).
03

Simplify the equation

Now we can simplify the equation further. Since raising a number to the power of 3 and then taking the cube root are inverse operations, they will cancel each other out on the left side, resulting in \(x\). On the right side, \(2^3 = 8\). Thus, we have \(x = 8\).
04

State the final simplified equation

The final simplified equation, without the radical, is \(x = 8\).

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Most popular questions from this chapter

What does it mean to rationalize the denominator of a radical expression?

Rationalize the denominator of each expression. $$\frac{1}{\sqrt{5}}$$

Simplify completely. $$\frac{18-6 \sqrt{7}}{6}$$

Rationalize the denominator of each expression. Assume all variables represent positive real numbers. $$\frac{9}{\sqrt[5]{a^{3}}}$$

Find each root, if possible. $$\sqrt{1-9}$$
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