Question

Find all the real square roots of 0.0625.

-0.25 and 0.25
-0.025 and 0.025
0.25
-0.025

Answer 1

The real square roots of 0.0625 are -0.25 and 0.25, as both of these numbers squared equal 0.0625.

Step-by-step explanation:

The student has asked to find all the real square roots of 0.0625. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we're looking for a number which, when squared, equals 0.0625.

To find this, we can recognize that the square root of 0.0625 could be thought of in fraction form as the square root of 625/10000, which simplifies to the square root of 625 divided by the square root of 10000. This reduces to 25/100 because 625 is a perfect square (25 * 25) and 10000 is also a perfect square (100 * 100). Therefore, the principal square root of 0.0625 is 0.25.

However, since every positive number has two square roots, one positive and one negative, and because the square of both -0.25 and 0.25 gives 0.0625, we conclude that the real square roots of 0.0625 are -0.25 and 0.25.

Answer 2

Factor

0.0625
0.25 * 0.25

Square root is a 2nd root which is even so there can be negative solutions.

Sqrt(0.0625) = 0.25 or -0.25