When dealing with principal square roots, the focus is on the positive square root of a number. In this article, learn how to identify the principal square roots and understand why the principal square root of 25 is 5!
What Is a Principal Square Root? How Does It Apply to the Square Root of 25?
The principal square root refers to the positive square root of a number. Recall that taking the square root is simply the process of reversing the process of squaring a number. Every nonnegative number has two square roots: the positive and negative roots. When dealing with the principal square root, focus on the positive root alone.
To better understand the concept of square roots and principal square roots, take a look at the square root of 25. 25 is a perfect square and is the result of squaring either -5 or 5.
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The square root of 25 is equal to -5 and 5, so the principal square root of 25 is equal to 25. The concept of principal square root applies to both a perfect square and a nonperfect square number - as long as they’re real and nonnegative. Here are examples of numbers with their square roots and principal square root:
You can see that whether you’re working with perfect squares and nonperfect squares, there will always be one principal square root.