Harrington Coleman
10/21/2023 · Middle School
1. Show that : \( (\sqrt{3}+\sqrt{2}) 3+(\sqrt{3}-\sqrt{2}) 3=18 \sqrt{3} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To show that
\[
(\sqrt{3}+\sqrt{2}) 3 + (\sqrt{3}-\sqrt{2}) 3 = 18 \sqrt{3},
\]
we can start by simplifying the left-hand side.
First, we can factor out the common term \(3\):
\[
3 \left( (\sqrt{3}+\sqrt{2}) + (\sqrt{3}-\sqrt{2}) \right).
\]
Next, we simplify the expression inside the parentheses:
\[
(\sqrt{3}+\sqrt{2}) + (\sqrt{3}-\sqrt{2}) = \sqrt{3} + \sqrt{2} + \sqrt{3} - \sqrt{2} = 2\sqrt{3}.
\]
Now, substituting this back into our expression gives:
\[
3 \cdot 2\sqrt{3} = 6\sqrt{3}.
\]
However, we need to check if this equals \(18\sqrt{3}\). It seems there was a misunderstanding in the original equation.
Let's re-evaluate the original expression:
\[
(\sqrt{3}+\sqrt{2}) 3 + (\sqrt{3}-\sqrt{2}) 3 = 3(\sqrt{3}+\sqrt{2} + \sqrt{3}-\sqrt{2}) = 3(2\sqrt{3}) = 6\sqrt{3}.
\]
Thus, we find that:
\[
6\sqrt{3} \neq 18\sqrt{3}.
\]
Therefore, the statement
\[
(\sqrt{3}+\sqrt{2}) 3 + (\sqrt{3}-\sqrt{2}) 3 = 18 \sqrt{3}
\]
is incorrect. The correct simplification shows that the left-hand side equals \(6\sqrt{3}\).
Quick Answer
The statement is incorrect. The left-hand side simplifies to \(6\sqrt{3}\), not \(18\sqrt{3}\).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
(0)
Ask Real Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
PREV 
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Uploaded Files
xxxx.png0%
Submit
