The problem asks to determine if the given mathematical statements are correct. If a statement is incorrect, correct it. If it is correct, write "correct". The statements are: 1. The square root of 36 is 6.

1. Problem Description

The problem asks to determine if the given mathematical statements are correct. If a statement is incorrect, correct it. If it is correct, write "correct". The statements are:

1. The square root of 36 is

6.

2. $\sqrt{(-7)^2} = -7$.

3. $\sqrt{25} = \pm 5$.

4. $\sqrt{8} \times \sqrt{8} = 8$.

5. $\sqrt{18} = 2\sqrt{3}$.

2. Solution Steps

1. The square root of 36 is both 6 and -6, since $6^2 = 36$ and $(-6)^2 = 36$. Therefore, the statement "The square root of 36 is 6" is incorrect. It should be $\pm 6$.

2. $\sqrt{(-7)^2} = \sqrt{49} = 7$. Therefore, the statement $\sqrt{(-7)^2} = -7$ is incorrect. It should be

7.

3. $\sqrt{25}$ refers to the principal square root, which is the positive square root. Thus, $\sqrt{25} = 5$, not $\pm 5$. Therefore, the statement $\sqrt{25} = \pm 5$ is incorrect. It should be

5.

4. $\sqrt{8} \times \sqrt{8} = (\sqrt{8})^2 = 8$. Therefore, the statement $\sqrt{8} \times \sqrt{8} = 8$ is correct.

5. $\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}$. Therefore, the statement $\sqrt{18} = 2\sqrt{3}$ is incorrect. It should be $3\sqrt{2}$.

3. Final Answer

1. $\pm 6$

2. $7$

3. $5$

4. correct

5. $3\sqrt{2}$