Vocabulary
Square Root- If b^2=a, then b is a square root of a. The radical symbol √ represents a non-negative square root.
Radical- An expression of the form √s or ⁿ√s where s is a number or an expression.
Radicand- The number or expression beneath a radical sign.
Rationalizing the Denominator- The process of eliminating a radical expression in the denominator of a fraction by multiplying both the numerator and denominator by an appropriate radical expression.
Conjugates- The expressions a+√b and a-√b where a and b are rational numbers
Radical- An expression of the form √s or ⁿ√s where s is a number or an expression.
Radicand- The number or expression beneath a radical sign.
Rationalizing the Denominator- The process of eliminating a radical expression in the denominator of a fraction by multiplying both the numerator and denominator by an appropriate radical expression.
Conjugates- The expressions a+√b and a-√b where a and b are rational numbers
Essential Information
Properties of Square Roots (a>0, b>0)
Simplifying Square Roots
The properties can be used to simplify expressions containing square roots.
Square root expressions are simplified if:
Rationalizing the Denominator
The properties can be used to simplify expressions containing square roots.
Square root expressions are simplified if:
- No radicand has a perfect square factor other than 1
- There is no radical in the denominator
Rationalizing the Denominator
The process in which the numerator and denominator are multiplied by the expressions in the table is called rationalizing the denominator. The expressions a + √(b) and a - √(b) are called conjugates of each other. Their product is always a rational number.
Solving Quadratic Equations
Square roots can be used to solve some types of quadratic equations. If s>0, then the equation x² = s has two real-number solutions: x=√(s) and x=-√(s). These solutions can be written as x=±√(s). (plus minus square root of s).
Square roots can be used to solve some types of quadratic equations. If s>0, then the equation x² = s has two real-number solutions: x=√(s) and x=-√(s). These solutions can be written as x=±√(s). (plus minus square root of s).