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

Demonstrate an understanding of factors of whole numbers

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Prime factorization

Number properties: Prime or Composite

Number properties: Prime?

Prime factors – Word Problem

Greatest common factors (GCF)

Greatest Common Factor 2 Numbers

Greatest Common Factor 2 Numbers – Word Problem

Least common multiple (LCM)

Lowest Common Multiple - 2 Numbers – Word Problem

Lowest Common Multiple 2 Numbers

Square and square roots

Square Root of a Perfect Square

Cubic and cube roots

Cube root of a perfect cube

Demonstrate an understanding of irrational numbers

Evaluating and simplifying radicals

Rational vs. Irrational numbers

Converting radicals to mixed radicals

Converting radicals to entire radicals

Demonstrate an understanding of powers with integral and rational exponents

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Simplify the power

Negative exponent rule

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

Demonstrate an understanding of multiplication of polynomial expressions

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Applications of polynomials

Demonstrate an understanding of common factors and trinomial factoring

Factoring polynomials: ax^2 + bx + c

Factoring Polynomials: ax^2 + bx + c

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Factoring perfect square trinomials

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Find the difference of squares

Word problems of polynomials

Common factors of polynomials

Factoring polynomials by grouping

Factoring polynomials: x^2 + bx + c

Interpret and explain the relationships among data, graphs and situations

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Solve problems involving systems of linear equations in two variables

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

Demonstrate an understanding of relations and functions

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Function notation

Demonstrate an understanding of slope

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Rate of change

Describe and represent linear relations

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

General form:  Ax  + By  + C = 0

General form: Ax + By + C = 0

Point-slope form: y - y_1 = m(x - x_1)

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Determine the characteristics of the graphs of linear relations

Introduction to linear equations

Introduction to nonlinear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel and perpendicular lines in linear functions

Relate linear relations expressed in various forms

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Applications of linear relations

Applications of linear equations

Solving systems of linear equations by elimination

Determine the equation of a linear relation

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Solving systems of linear equations by substitution

Solve problems involving distance between two points and midpoint of a line segment

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Use tangent ratio to calculate angles and sides (Tan = o / a)

Represent a linear function using function notation

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Number Relations and Functions 10

Algebra and Number

Relations and Functions

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>. 

Converting radicals to mixed surds

How to convert radicals to mixed radicals

Estimating square roots