What are the square roots of 75?
Understand the Problem
The question is asking for the value of the square roots of the number 75, which will involve identifying both the positive and negative square roots.
Answer
$5\sqrt{3}$ and $-5\sqrt{3}$
Answer for screen readers
The square roots of 75 are $5\sqrt{3}$ and $-5\sqrt{3}$
Steps to Solve
- Identify the positive square root
The positive square root of 75 is given by the positive solution to the equation $\sqrt{75}$.
- Simplify under the radical
We can simplify the square root by finding the prime factorization of 75: $75 = 3 \times 25 = 3 \times 5^2$. So the square root can be simplified as follows:
$$\sqrt{75} = \sqrt{3 \times 5^2} = 5 \sqrt{3}$$
- Consider both positive and negative roots
Remember that every positive number has two square roots: one positive and one negative. Hence, the square roots of 75 are:
The positive root is $5 \sqrt{3}$, and the negative root is $-5 \sqrt{3}$.
The square roots of 75 are $5\sqrt{3}$ and $-5\sqrt{3}$
More Information
The square roots include both the positive and negative values.
Tips
One common mistake is to only consider the positive square root. Always remember to include both the positive and negative square roots.
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