square root of 38 simplified
Understand the Problem
The question is asking for the simplification of the square root of 38. To solve it, we need to determine if 38 can be factored into a perfect square and express the square root in its simplest form.
Answer
The simplest form of the square root of 38 is $\sqrt{38}$.
Answer for screen readers
The simplest form of the square root of 38 is $\sqrt{38}$.
Steps to Solve
- Find the factors of 38
First, let’s determine if 38 can be factored into any perfect squares. The numbers that multiply to give 38 are 1, 2, 19, and 38 itself.
- Identify perfect square factors
The only perfect square that is a factor of 38 is 1, since $1^2 = 1$ is a perfect square, and $2^2 = 4$ and $3^2 = 9$ and so on are greater than 1.
- Express the square root including the factor
Since 38 can be expressed as $38 = 1 \times 38$, we can write the square root as: $$ \sqrt{38} = \sqrt{1 \times 38} $$
- Simplify the square root
Now, we take the square root of the perfect square factor: $$ \sqrt{38} = \sqrt{1} \times \sqrt{38} = 1 \times \sqrt{38} $$
Since we cannot simplify it further, we keep it as: $$ \sqrt{38} $$
- Estimate the square root for better understanding
For a numerical approximation, use a calculator to find that: $$ \sqrt{38} \approx 6.16 $$
The simplest form of the square root of 38 is $\sqrt{38}$.
More Information
The square root of 38 cannot be simplified into a simpler form using perfect squares. It is approximately 6.16 when calculated numerically. Understanding square roots and perfect squares can help simplify such problems in the future.
Tips
- A common mistake is trying to further simplify $\sqrt{38}$ by misidentifying other factors. Remember, unless you find a perfect square factor, the simplest form is just $\sqrt{38}$.
