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

G.SO.2201G1

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

G.SO.2201G2

Pairs of lines and angles

G.SO.2201G3

auto-gen

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

M.SO.2201M1

Rate of change

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

M.SO.2201M2

Enlargements and reductions with scale factors

Scale diagrams

M.SO.2201M3

Similar triangles

Similar polygons

NL.SO.2201N1

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

NL.SO.2201N2

Set notation

Understanding How to Use Set Notation

Set builder notation

Intersection and union of 2 sets

Intersection and Union of 2 Sets

Intersection and union of 3 sets

Intersection and Union of 3 Sets

NL.SO.2201N3

Conversion between entire radicals and mixed radicals

Adding and subtracting radicals

Combining Like Radicals

Adding and Subtracting Radicals

Multiplying radicals

Multiplying Radicals

Operations with radicals

Operations with Radicals

Evaluating and simplifying radicals

Converting radicals to mixed radicals

Converting radicals to entire radicals

Adding radicals

Subtracting radicals

Multiplying and dividing radicals

Dividing radicals

Rationalize the denominator

NL.SO.2201N4

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

RF.SO.2201RF1

Characteristics of quadratic functions

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

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

RF.SO.2201RF2

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

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

RP.SO.2201RP1

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Sampling methods

Sampling Methods

Frequency distribution and histograms

Frequency polygons

S.SO.2201S1

Spread of a data set - standard deviation & variance

Measures of relative standing - z-score, quartiles, percentiles

Introduction to normal distribution

The Normal Distribution and the 68-95-99.7 Rule

Using "invNorm" to Solve Normal Distribution Problems

Normal distribution and continuous random variable

Z-scores and random continuous variables

S.SO.2201S2

Point estimates

Confidence levels and critical values

Margin of error

Margin of Error

Making a confidence interval

Confidence intervals to estimate population mean

Academic Mathematics 2201

Measurement

Number and Logic

Relations and Functions

Mathematics Research Project

math

Ex. 1:

Intro

<p>- 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?<br />
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.</p>


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>. 