Square Root
A square root of a number is the value that, when multiplied by itself, produces the original number. The square root of 25 is 5, written as the square root symbol over 25 equals 5, because 5 times 5 = 25. This Grade 7 math skill from Saxon Math, Course 2 introduces radical notation and builds number sense around perfect squares, preparing students for the Pythagorean theorem, quadratic equations, and any math or science context where squared quantities appear — from area calculations to physics formulas.
Key Concepts
Property If we know the area of a square, we can find the length of its side by finding the square root of the area. The square root symbol is $\sqrt{\phantom{x}}$. For example, since a 3 by 3 square has an area of 9, the square root of 9 is 3. $$ \sqrt{9} = 3 $$.
Examples To find the square root of 49, ask what number times itself equals 49. Since $7 \cdot 7 = 49$, we know that $\sqrt{49} = 7$. Squaring a number and finding its square root are inverse operations, so they undo each other. For example, $\sqrt{10^2} = \sqrt{100} = 10$. What is $\sqrt{144}$? We need a number that gives 144 when multiplied by itself. That number is 12, so $\sqrt{144} = 12$.
Explanation Think of finding a square root as a math mystery! You are given the final area of a square, and your mission is to uncover the original side length. You need to ask yourself, "What number, when I multiply it by itself, gives me this area?" It’s the ultimate reverse move of squaring a number, turning an area back into a length.
Common Questions
What is a square root?
A square root of a number is the value that when multiplied by itself gives that number. The square root of 36 is 6, because 6 times 6 = 36.
How do I find the square root of a number?
For perfect squares, recall multiplication facts: square root of 49 = 7 because 7 squared = 49. For non-perfect squares, use estimation or a calculator to find the decimal approximation.
What are perfect squares?
Perfect squares are integers that are the result of multiplying a whole number by itself. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Their square roots are whole numbers.
Can a negative number have a square root?
Not in the real number system, because squaring any real number (positive or negative) gives a positive result. The square roots of negative numbers are imaginary numbers, studied in advanced math.
When do students learn about square roots?
Square roots are typically introduced in Grade 7. Saxon Math, Course 2 covers them in Chapter 8 alongside exponents and number properties.
How does knowing square roots help in geometry?
The Pythagorean theorem gives the hypotenuse of a right triangle as the square root of (a squared + b squared). Knowing square roots is essential for finding side lengths in geometry problems.
What is the difference between a square and a square root?
Squaring a number multiplies it by itself (5 squared = 25). Taking the square root is the inverse operation — it asks which number was squared to get this result (square root of 25 = 5).