Principal Square Root
Learn how to find the principal square root by reversing the squaring operation, using the √ symbol to solve problems like √144 = 12 in Grade 6 math.
Key Concepts
Property Finding the principal square root of a number is the inverse operation of squaring a number. The symbol $\sqrt{\phantom{0}}$ asks, 'What positive number, when multiplied by itself, gives you the number inside?' $$ \sqrt{36} = 6 \text{ because } 6^2 = 36$$.
Examples $\sqrt{81} = 9$ $\sqrt{100} \sqrt{49} = 10 7 = 3$ A square shaped garden has an area of 144 square feet. The length of one side is $\sqrt{144} = 12$ feet.
Explanation Think of squaring as building a square patio. If you know one side is 7 feet, you square it to find the area is 49 square feet. The square root does the reverse! If you only know the patio's area is 49 square feet, the square root, $\sqrt{49}$, is your magic tool to find out that one side must be 7 feet long.
Common Questions
What is a principal square root in 6th grade math?
The principal square root of a number is the positive number that, when multiplied by itself, gives you the original number. For example, √36 = 6 because 6² = 36. It is the inverse operation of squaring a number.
How do you find the principal square root of a number?
To find the principal square root, ask yourself: what positive number multiplied by itself equals the number inside the √ symbol? For instance, √81 = 9 because 9 × 9 = 81. This is the reverse process of squaring a number.
How is the square root used in real life for Grade 6 students?
A common real-life example is finding the side length of a square when you know its area. If a square garden has an area of 144 square feet, you calculate √144 = 12 to find that each side is 12 feet long.
What does the √ symbol mean in Saxon Math Course 1?
In Saxon Math Course 1, the √ symbol is called the radical sign and it asks for the principal square root of the number inside it. It always refers to the positive square root, so √49 = 7, not -7.