3 square root of 125 simplified
Understand the Problem
The question is asking to simplify the expression involving the square root of 125 multiplied by 3. This involves finding the simplest form of the square root and presenting the final answer.
Answer
$15\sqrt{5}$
Answer for screen readers
The simplified form of the expression is $15\sqrt{5}$.
Steps to Solve
- Find the square root of 125
To simplify the expression, start by breaking down the square root of 125. Notice that 125 can be factored into $25 \times 5$.
So, we have:
$$ \sqrt{125} = \sqrt{25 \times 5} $$
- Simplify the square root
Next, simplify the square root. The square root of 25 is 5, so:
$$ \sqrt{125} = \sqrt{25} \times \sqrt{5} = 5\sqrt{5} $$
- Multiply by 3
Now, multiply the result by 3, as given in the problem:
$$ 3 \cdot \sqrt{125} = 3 \cdot 5\sqrt{5} $$
- Combine the results
Finally, combine the multiplication:
$$ 3 \cdot 5\sqrt{5} = 15\sqrt{5} $$
The simplified form of the expression is $15\sqrt{5}$.
More Information
When simplifying square roots, it's important to factor the number under the square root into perfect squares whenever possible. Here, knowing that $25$ is a perfect square allowed us to simplify $125$ neatly.
Tips
- Forgetting to simplify the square root first before multiplying.
- Incorrectly calculating the square root, especially with larger numbers.
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