The exact answer to the question "What is the square root of the root under 16?" is 4.
Understanding the Question
The phrasing "the root under 16" refers to the radicand, which is the number located beneath the radical symbol (√) in a mathematical expression. In this specific instance, the number under the root is 16. Therefore, the question asks to find the square root of 16.
Calculating the Square Root of 16
To find the square root of a number means to determine a value that, when multiplied by itself, yields the original number. For the number 16, we are looking for a number 'x' such that $x \times x = 16$.
The unique positive number that satisfies this condition is 4, because:
$4 \times 4 = 16$
Thus, the square root of 16 is 4.
Key Concepts of Square Roots
Square roots are fundamental operations in mathematics. When we refer to "the square root" of a positive number, we typically mean its principal square root, which is the positive value. For example, while both 4 and -4, when squared, result in 16 ($(-4) \times (-4) = 16$), the principal square root is conventionally taken as the positive value, 4.
Numbers whose square roots are integers are known as perfect squares. 16 is an example of a perfect square.
Examples of Perfect Squares
Number | Square Root | Calculation |
---|---|---|
1 | 1 | $1 \times 1 = 1$ |
4 | 2 | $2 \times 2 = 4$ |
9 | 3 | $3 \times 3 = 9$ |
16 | 4 | $4 \times 4 = 16$ |
25 | 5 | $5 \times 5 = 25$ |
The understanding of square roots is applied across various fields, including geometry for calculating side lengths of squares or hypotenuses in right triangles, and in physics for formulas involving areas and volumes. For example, if a square-shaped area measures 16 square units, its side length must be 4 units.
For more detailed information on understanding and calculating square roots, you can explore resources covering the square root of 16.