What is the following quotient?

[tex]\[
\frac{\sqrt[3]{60}}{\sqrt[3]{20}}
\][/tex]

A. [tex]\(\sqrt[3]{3}\)[/tex]

B. 3

C. [tex]\(2(\sqrt[3]{5})\)[/tex]

D. 40



Answer :

Certainly! Let's tackle this problem step-by-step.

Given the quotient to simplify:
[tex]\[ \frac{\sqrt[3]{60}}{\sqrt[3]{20}} \][/tex]

#### Step 1: Calculate the cube roots

We first need to find the cube roots of the numbers 60 and 20.

1. The cube root of 60:
[tex]\[ \sqrt[3]{60} \approx 3.9148676411688634 \][/tex]

2. The cube root of 20:
[tex]\[ \sqrt[3]{20} \approx 2.7144176165949063 \][/tex]

#### Step 2: Form the quotient

We then form the quotient by dividing the cube root of 60 by the cube root of 20:
[tex]\[ \frac{\sqrt[3]{60}}{\sqrt[3]{20}} = \frac{3.9148676411688634}{2.7144176165949063} \approx 1.4422495703074085 \][/tex]

#### Step 3: Simplify the quotient

Finally, we express the simplified quotient in a more recognizable form. This quotient can also be rewritten as:
[tex]\[ 2(\sqrt[3]{5}) = 2 \times \sqrt[3]{20} \][/tex]
where:
[tex]\[ 2 \times 2.7144176165949063 \approx 5.428835233189813 \][/tex]

Thus, the values we have are:
[tex]\[ \sqrt[3]{60} \approx 3.9148676411688634 \][/tex]
[tex]\[ \sqrt[3]{20} \approx 2.7144176165949063 \][/tex]
[tex]\[ \frac{\sqrt[3]{60}}{\sqrt[3]{20}} \approx 1.4422495703074085 \][/tex]
[tex]\[ 2 \times \sqrt[3]{20} \approx 5.428835233189813 \][/tex]

So, the given quotient
[tex]\[ \frac{\sqrt[3]{60}}{\sqrt[3]{20}} \approx 1.4422495703074085 \][/tex]

This is the simplified form of the quotient given in the problem.

Hopefully, this clarifies the solution for you! If you need further assistance, feel free to ask.