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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

  1. 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.

  1. Divide 4 by the square root of 2

Now, we divide 4 by the value we obtained from the square root of 2:

$$ \frac{4}{\sqrt{2}} $$

  1. Rationalize the denominator

To simplify the division, we can multiply both the numerator and the denominator by $ \sqrt{2} $:

$$ \frac{4 \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{4 \cdot \sqrt{2}}{2} $$

  1. 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.
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