3 divided by the square root of 3
Understand the Problem
The question is asking for the mathematical operation of dividing 3 by the square root of 3. To solve this, we will calculate the square root of 3 and then perform the division.
Answer
$\sqrt{3}$
Answer for screen readers
The final answer is $\sqrt{3}$.
Steps to Solve
- Calculate the Square Root of 3
First, we need to find the square root of 3. The square root of a number $x$ is the number that, when multiplied by itself, gives $x$.
$$ \sqrt{3} $$
- Perform the Division
Next, we will divide 3 by the square root of 3. This means we are taking the result of the square root and dividing it into 3.
$$ \frac{3}{\sqrt{3}} $$
- Rationalize the Denominator
To simplify our answer, we can rationalize the denominator. This means we will multiply both the numerator and the denominator by $\sqrt{3}$.
$$ \frac{3 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} = \frac{3\sqrt{3}}{3} $$
- Simplify the Expression
Now, we simplify the expression by canceling out the 3 in the numerator and denominator.
$$ \sqrt{3} $$
The final answer is $\sqrt{3}$.
More Information
The square root of 3 is an irrational number, approximately equal to 1.732. Dividing by the square root of a number is a common operation in mathematics that often leads to simplifying expressions.
Tips
- Forgetting to rationalize the denominator can lead to an incorrect final expression.
- Not using the correct order of operations, such as attempting to compute the square root incorrectly before performing the division.