key term - Square Root

Definition

The square root, denoted by the symbol √, is a mathematical operation that represents the inverse of squaring a number. It is the value that, when multiplied by itself, gives the original number. The square root of a number is one of the two equal factors of that number.

5 Must Know Facts For Your Next Test

1. The square root of a number is the value that, when multiplied by itself, gives the original number.
2. Square roots can be used to simplify expressions, solve equations, and work with rational exponents.
3. The square root property states that if $x^2 = a$, then $x = \pm \sqrt{a}$.
4. Quadratic equations can be solved using the square root property or the quadratic formula, both of which involve square roots.
5. Rational exponents can be used to represent square roots, where $a^{1/2} = \sqrt{a}$.

Review Questions

• Explain how square roots can be used to simplify expressions.
  • Square roots can be used to simplify expressions by rewriting them in terms of perfect squares. For example, $\sqrt{16}$ can be simplified to 4, as 4 is the value that, when multiplied by itself, gives 16. This principle can be applied to more complex expressions involving square roots to simplify them and make them easier to work with.
• Describe how the square root property is used to solve equations with square roots.
  • The square root property states that if $x^2 = a$, then $x = \pm \sqrt{a}$. This property can be used to solve equations involving square roots by isolating the square root term and then taking the square root of both sides of the equation. For example, to solve the equation $x^2 = 25$, we can apply the square root property to get $x = \pm \sqrt{25} = \pm 5$.
• Analyze the relationship between square roots and rational exponents, and explain how they are used to solve quadratic equations.
  • Rational exponents can be used to represent square roots, where $a^{1/2} = \sqrt{a}$. This relationship is important when solving quadratic equations using the quadratic formula, which involves square roots. The quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, uses square roots to find the solutions to a quadratic equation. Additionally, the square root property can be used to solve quadratic equations by isolating the square root term and taking the square root of both sides.

Related terms

Radical:

The symbol √ used to represent the square root operation.

Perfect Square:

A number that is the square of an integer, such as 4, 9, 16, etc.

Irrational Number:

A number that cannot be expressed as a simple fraction, such as √2 or √3, which have decimal expansions that never terminate or repeat.