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.
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.
