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

  1. 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 $x$.

$$ \sqrt{3} $$

  1. 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.

$$ \frac{3}{\sqrt{3}} $$

  1. Rationalize the Denominator

To simplify our answer, we can rationalize the denominator. This means we will multiply both the numerator and the denominator by $\sqrt{3}$.

$$ \frac{3 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} = \frac{3\sqrt{3}}{3} $$

  1. 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.
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