As illustrated below, this application will identify the largest perfect square factor of the radicand. If the largest perfect square factor is greater than 1, it will apply the product rule for radicals to find the square root of the radicand in simplified form and its decimal equivalent to four places. It will also return the square root of a perfect square such as 16.
Students in the 9th grade should be able to find the square root of a number that is a perfect square under Common Core standards. For example, the square root of 16 (√16 ) equals 4 because 4 * 4 = 42 = 16. As a result, 16 is a perfect square. With respect to additional math vocabulary, 16 is the radicand under the radical symbol (√ ) in the radical expression √16.
Knowing when a number is a perfect square and a factor of another number (perfect square factor) will facilitate the simplification of the square root of a number that is not a perfect square under the product rule for radicals. For example, 32 is not a perfect square because no whole number multiplied by itself equals 32. But 16 is a factor of 32 because 16 * 2 = 32. As noted above, 16 is also a perfect square because 42 = 16. Therefore, 16 is a perfect square factor of 32. Notably, 4 is also a perfect square factor of 32 since 22 = 4, and 4 * 8 = 32. However, 16 is the largest perfect square factor of 32. And under the product rule for radicals:
√32 = √16*2 = √16 * √2 = 4*√2 = 4√2.
As indicated by the example of 32, knowing the factors and corresponding factor pairs of a number is essential to simplifying its square root efficiently. Notably, the simplified square root is also the exact value of the square root.
The Other Side
On the other side of knowing how to find the exact value of the square root of a non-negative number is knowing how to find the hypotenuse of a right triangle given its leg lengths, find the distance between two points on a coordinate plane, solving quadratic equations, and much more. In short, knowing how to find the exact value of the square root of a number is very important.