Definition of a Square Root
This Grade 6 algebra skill from Yoshiwara Elementary Algebra introduces the definition of a square root. Students learn that the square root of a number n is the non-negative value x such that x^2 = n. They distinguish between perfect and non-perfect square roots and understand the square root symbol (radical sign).
Key Concepts
Property The number $s$ is called a square root of a number $b$ if $s^2 = b$. Every positive number has two square roots, one positive and one negative.
Examples The two square roots of 49 are 7 and 7, because $7^2 = 49$ and $( 7)^2 = 49$. A square garden has an area of 64 square feet. Its side length is a square root of 64, which is 8 feet. Since $12^2 = 144$, we know that 12 is a square root of 144. The other square root is $ 12$.
Explanation Finding a square root is the reverse of squaring a number, like finding a square's side from its area.
Common Questions
What is a square root?
The square root of a number n is the non-negative value x such that x squared equals n. For example, the square root of 25 is 5 because 5^2 = 25.
What is the square root symbol called?
The symbol is called the radical sign. The expression under the radical is called the radicand.
What is the difference between a perfect and non-perfect square root?
A perfect square has a whole number square root (like sqrt(16) = 4). A non-perfect square has an irrational square root (like sqrt(2) which is approximately 1.414).
Can a square root be negative?
The principal (main) square root is always non-negative. However, the equation x^2 = 9 has two solutions: x = 3 and x = -3.
Where is the definition of square root taught?
The definition of a square root is introduced in the Yoshiwara Elementary Algebra textbook for Grade 6.