# 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.

$5\sqrt{3}$ and $-5\sqrt{3}$

The square roots of 75 are $5\sqrt{3}$ and $-5\sqrt{3}$

#### Steps to Solve

1. Identify the positive square root

The positive square root of 75 is given by the positive solution to the equation $\sqrt{75}$.

1. 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:

$$\sqrt{75} = \sqrt{3 \times 5^2} = 5 \sqrt{3}$$

1. 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 $-5\sqrt{3}$