Which statements about square roots are true? Check all that apply.

Question

The square root of a positive number cannot be negative.
All positive numbers have two square roots.
StartRoot 18 EndRoot= 9 because 9(2) = 18.
StartRoot 49 EndRoot= 7 because 7(7) = 49.
StartRoot 25 EndRoot = 5 because 52= 25.

Answer 1

Let's evaluate each of the statements one by one:

1. The square root of a positive number cannot be negative.

   • True. The principal square root of a positive number is always non-negative.

2. All positive numbers have two square roots.

   • True. Every positive number has one positive square root and one negative square root. For example, √4 = 2 and -2 are both square roots of 4.

3. √18 = 9 because 9(2) = 18.

   • False. The correct square root of 18 is approximately 4.24, as 4.24 × 4.24 ≈ 18, not 9.

4. √49 = 7 because 7(7) = 49.

   • True. The square root of 49 is indeed 7, since 7 × 7 = 49.

5. √25 = 5 because 5² = 25.

   • True. The square root of 25 is 5, as 5 × 5 = 25.

In summary, the true statements are:

• The square root of a positive number cannot be negative.
• All positive numbers have two square roots.
• √49 = 7 because 7(7) = 49.
• √25 = 5 because 5² = 25.