Algebra Tutorials!  
Monday 24th of June
Rotating a Parabola
Multiplying Fractions
Finding Factors
Miscellaneous Equations
Mixed Numbers and Improper Fractions
Systems of Equations in Two Variables
Literal Numbers
Adding and Subtracting Polynomials
Subtracting Integers
Simplifying Complex Fractions
Decimals and Fractions
Multiplying Integers
Logarithmic Functions
Multiplying Monomials
The Square of a Binomial
Factoring Trinomials
The Pythagorean Theorem
Solving Radical Equations in One Variable
Multiplying Binomials Using the FOIL Method
Imaginary Numbers
Solving Quadratic Equations Using the Quadratic Formula
Solving Quadratic Equations
Order of Operations
Dividing Complex Numbers
The Appearance of a Polynomial Equation
Standard Form of a Line
Positive Integral Divisors
Dividing Fractions
Solving Linear Systems of Equations by Elimination
Multiplying and Dividing Square Roots
Functions and Graphs
Dividing Polynomials
Solving Rational Equations
Use of Parentheses or Brackets (The Distributive Law)
Multiplying and Dividing by Monomials
Solving Quadratic Equations by Graphing
Multiplying Decimals
Use of Parentheses or Brackets (The Distributive Law)
Simplifying Complex Fractions 1
Adding Fractions
Simplifying Complex Fractions
Solutions to Linear Equations in Two Variables
Quadratic Expressions Completing Squares
Dividing Radical Expressions
Rise and Run
Graphing Exponential Functions
Multiplying by a Monomial
The Cartesian Coordinate System
Writing the Terms of a Polynomial in Descending Order
Quadratic Expressions
Solving Inequalities
Solving Rational Inequalities with a Sign Graph
Solving Linear Equations
Solving an Equation with Two Radical Terms
Simplifying Rational Expressions
Intercepts of a Line
Completing the Square
Order of Operations
Factoring Trinomials
Solving Linear Equations
Solving Multi-Step Inequalities
Solving Quadratic Equations Graphically and Algebraically
Collecting Like Terms
Solving Equations with Radicals and Exponents
Percent of Change
Powers of ten (Scientific Notation)
Comparing Integers on a Number Line
Solving Systems of Equations Using Substitution
Factoring Out the Greatest Common Factor
Families of Functions
Monomial Factors
Multiplying and Dividing Complex Numbers
Properties of Exponents
Multiplying Square Roots
Adding or Subtracting Rational Expressions with Different Denominators
Expressions with Variables as Exponents
The Quadratic Formula
Writing a Quadratic with Given Solutions
Simplifying Square Roots
Adding and Subtracting Square Roots
Adding and Subtracting Rational Expressions
Combining Like Radical Terms
Solving Systems of Equations Using Substitution
Dividing Polynomials
Graphing Functions
Product of a Sum and a Difference
Solving First Degree Inequalities
Solving Equations with Radicals and Exponents
Roots and Powers
Multiplying Numbers
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Adding and Subtracting Square Roots

We’ve already covered the addition and subtraction of numerical square roots in some detail. The procedure for adding and subtracting square roots which may contain algebraic expressions is more or less the same:

  • simplify the square root in each term of the expression
  • combine terms whose square roots are identical

We will illustrate this strategy with a number of simple examples.

Example 1:



The square roots in all four of the terms in this expression are identical, all being just . So, we just collect the “like terms":

as the simplest form of the result.


Example 2:



Neither of the two square roots occurring here are in simplest form. So, to start, we must simplify each term.


8x 3 = 2 3x 3 = 2 2 · 2 · x 2 · x

we can write


18x 5 = 2 · 3 2 · (x 2) 2 x

and so


You could leave the final answer as this last expression, or you could still do a bit of factoring to get, as the most simplified form


Example 3:



This example is very similar to Example 2 above, so you should use it as a practice problem. Try to solve it yourself before looking at our solution, given below.

First, simplify the individual square roots where possible. Since

18x 2 = 2 · 3 2 · x 2

we get

and since

50x 4 = 2 · 5 2 · (x 2) 2

we get


as the final answer.


Example 4:



The last three of the square roots here can be simplified slightly:



as the final result.



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