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Master Converting Radicals to Mixed Radicals | Step-by-Step

PC20.1

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Absolute value functions

Expressing an Absolute Value Linear Function as a Piecewise Function

Expressing an Absolute Value Quadratic Function as a Piecewise Function

Solving absolute value equations

Solving absolute value inequalities

Solving Absolute Value Inequalities Involving "less than"

Solving Absolute Value Inequalities Involving "greater than"

Recognizing Absolute Value Inequalities with "No Solution" or "All Real Numbers"

PC20.10

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Geometric sequences

Geometric series

Geometric Series

Infinite geometric series

Sigma notation

PC20.11

Graphing reciprocals of linear functions

Graphs of rational functions

Graphing reciprocals of quadratic functions

PC20.2

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

Evaluating and simplifying radicals

Converting radicals to mixed radicals

Converting radicals to entire radicals

Adding and subtracting radicals

Adding radicals

Subtracting radicals

Multiplying and dividing radicals

Dividing radicals

Multiplying radicals

Rationalize the denominator

PC20.3

Solving rational equations

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Adding and Subtracting Rational Expressions

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Applications of rational equations

PC20.4

Unit circle

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

PC20.5

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

PC20.6

Factoring difference of cubes

Factoring sum of cubes

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

PC20.7

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Solving a quadratic equation with TWO REAL SOLUTIONS

Solving a quadratic equation with TWO COMPLEX SOLUTIONS

Quadratic function in vertex form: y = a(x-p)^2 + q

Completing the square

Completing the Square

PC20.8

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

PC20.9

Solving quadratic inequalities

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Graphing systems of linear inequalities

Applications of inequalities

Pre-Calculus 20

Number Sense

math

Ex. 1:

Intro

- Okay, so welcome to this question right here. We have a 7 over 11, multiplied by radical 1250. So, the number outside of the radical you can actually just keep it as it is and you can write it out in terms of a fraction like this, right? And you just have to leave it alone, just for now. And the 1250, because the number kind of gets too big, so what I suggest is actually figure out the prime factorization for this guy. So, let's do the 1250 on the side and let's go ahead, let's do the 5. If you divide the number by 5, you've got a 250 right here. And if you do it one more time, you're gonna get yourself other numbers like the 50 here and divided by 5 you get yourself a 10, and if you divide it by 5 again you get yourself a 2. the 1250 is just 5 x 5 x 5 x 5 x 2 right? 
So, the trick is if you're doing the square root, that means this root number here is a 2, right? So, for every pair of identical number, in this case we have a pair of 5 here, and a pair of 5 here, they can be taken out from the radical sign an put in the front. Now, the question now becomes, there's a 5 in the front because there's a pair in here, and there's another 5 you just took out from the radical, and you're just left with the 2 inside of the radical. And you just have to work out the math, if you do the math correctly which is 7 over 11, x 5 x 5 and then x root 2. You get yourself 175 over 11, and there's your root 2. And that's the end for our discussion. Thanks for watching.

In this session, we will learn how to convert <a href='[[glossary.html|{"keyword":"Radical"}]]'>radicals</a> to mixed radicals. When the content inside the radical sign is a number, you can do the conversion by performing prime factorization. We will also learn how to do the conversion when the content inside the radical sign is a <a href="[[glossary.html|{"keyword":"Variable"}]]">variable</a>.