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What Is the List of Perfect Squares, and Why Do I Need It?

list of perfect squares: Boy writing a mathematical equation on the blackboard

Students at all levels of math need a list of perfect squares. Knowing the most common perfect squares makes it much easier to solve square roots, which show up in all kinds of math problems. But before we go into perfect squares, let's review the definition of square roots.

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What Is the Definition of a Linear Expression?

linear expression: equations on a grid paper

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

For example, is a variable raised to the second power, but x is a variable raised to the first power.

5 is an example of a constant.

Note that the coefficients in front of the variables don't matter. Let's take a couple of these polynomials (a polynomial just means an expression with two or more terms) as examples.

2x - y + 3 is a linear expression.

x + y + z⁵ is a non-linear expression. It contains a term raised to the fifth power.

4 - 2 is a linear expression.

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What Is the Distributive Property of Multiplication?

distributive property of multiplication: girl taking notes while looking at her laptop

The distributive property of multiplication is a property of real numbers that shows how we can break apart multiplication problems into separate terms. The property states that an algebraic expression a(b + c) becomes ab + ac. In other words, the multiplication of a distributes to both variables inside the parentheses, b and c.

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Why Are Repeating Decimals Rational Numbers?

are repeating decimals rational: DECIMAL spelled using wooden blocks

Are repeating decimals rational? The answer is yes. But before we talk about why, let's review rational numbers. A rational number is a fraction in its lowest term. It's written in form a/b, where both a and b are integers, and b is a non-zero denominator.

Now, let’s talk about why repeating decimals are considered rational numbers.

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Vertical Angle Theorem: What It Is and How to Use It

The Vertical Angle Theorem says the opposing angles of two intersecting lines must be congruent, or identical in value. That means no matter how or where two straight lines intersect each other, the angles opposite to each other will always be congruent, or equal in value:

Vertical Angle Theorem: Graph showing two straight lines intersect each other

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