Simplify the term (3)/(sqrt(3)).
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Simplify the term $\frac{3}{\sqrt{3}}$.
To rationalize the denominator, multiply the numerator and denominator by $\sqrt{3}$.
$$ \frac{3}{\sqrt{3}} = \frac{3 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}} = \frac{3\sqrt{3}}{3} = \sqrt{3} $$
Step 2: Substitute the simplified term back into the original expression.
The expression becomes:
$$ \sqrt{3} \left( \sqrt{3} - \frac{2\sqrt{3}}{3} \right) $$
Step 3: Distribute $\sqrt{3}$ into the terms inside the parenthesis.
$$ \left( \sqrt{3} \times \sqrt{3} \right) - \left( \sqrt{3} \times \frac{2\sqrt{3}}{3} \right) $$
Step 4: Calculate each term.
For the first term:
$$ \sqrt{3} \times \sqrt{3} = 3 $$
For the second term:
$$ \sqrt{3} \times \frac{2\sqrt{3}}{3} = \frac{2 \times (\sqrt{3} \times \sqrt{3})}{3} = \frac{2 \times 3}{3} = \frac{6}{3} = 2 $$
Step 5: Subtract the second term from the first term.
$$ 3 - 2 = 1 $$
The final answer is $\boxed{1}$.
