Sure! Let's solve the problem of finding the sum of [tex]\(2 \sqrt{5}\)[/tex] and [tex]\(3 \sqrt{7}\)[/tex].
### Step-by-Step Solution:
1. Identify the components:
First, we need to identify each term that we're working with:
[tex]\[
\text{Term 1} = 2 \sqrt{5}
\][/tex]
[tex]\[
\text{Term 2} = 3 \sqrt{7}
\][/tex]
2. Calculate the value of each term:
- For the first term, [tex]\(2 \sqrt{5}\)[/tex]:
[tex]\[
2 \sqrt{5} \approx 2 \times 2.236067977 \approx 4.472135955
\][/tex]
- For the second term, [tex]\(3 \sqrt{7}\)[/tex]:
[tex]\[
3 \sqrt{7} \approx 3 \times 2.645751311 \approx 7.937253933
\][/tex]
3. Summing the terms:
Now, let's add these two terms together:
[tex]\[
2 \sqrt{5} + 3 \sqrt{7} \approx 4.472135955 + 7.937253933
\][/tex]
4. Calculate the sum:
Perform the addition:
[tex]\[
4.472135955 + 7.937253933 = 12.409389888
\][/tex]
5. Conclusion:
Therefore, the sum of [tex]\(2 \sqrt{5}\)[/tex] and [tex]\(3 \sqrt{7}\)[/tex] is approximately:
[tex]\[
12.409389888
\][/tex]
The terms are:
[tex]\[
2 \sqrt{5} \approx 4.472135955
\][/tex]
[tex]\[
3 \sqrt{7} \approx 7.937253933
\][/tex]
And their sum:
[tex]\[
2 \sqrt{5} + 3 \sqrt{7} \approx 12.409389888
\][/tex]
