4 divided by the square root of 2
Understand the Problem
The question is asking for the value of 4 divided by the square root of 2. To solve this, we will calculate the square root of 2 and then divide 4 by that value.
Answer
$ 2\sqrt{2} $
Answer for screen readers
The value of $ \frac{4}{\sqrt{2}} $ is $ 2\sqrt{2} $.
Steps to Solve
- Calculate the square root of 2
First, we find the square root of 2, which can be expressed as:
$$ \sqrt{2} $$
The approximate value of $ \sqrt{2} $ is about 1.414.
- Divide 4 by the square root of 2
Now, we divide 4 by the value we obtained from the square root of 2:
$$ \frac{4}{\sqrt{2}} $$
- Rationalize the denominator
To simplify the division, we can multiply both the numerator and the denominator by $ \sqrt{2} $:
$$ \frac{4 \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{4 \cdot \sqrt{2}}{2} $$
- Simplify the expression
Now, simplify the expression by dividing 4 by 2:
$$ \frac{4 \cdot \sqrt{2}}{2} = 2\sqrt{2} $$
The value of $ \frac{4}{\sqrt{2}} $ is $ 2\sqrt{2} $.
More Information
The square root of 2 is an irrational number that has many practical applications, especially in geometry and trigonometry. The simplified form $ 2\sqrt{2} $ is often preferred in mathematical contexts.
Tips
- Forgetting to rationalize the denominator when dividing by a square root.
- Not using the correct approximation for $ \sqrt{2} $; it is important to use the exact form where possible.