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

8.EE.A.1

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Using exponents to describe numbers

Expanded powers

Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with 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

8.EE.A.2

Squares and square roots

Square Root of a Perfect Square

Square and square roots

Cubic and cube roots

Cube root of a perfect cube

Converting radicals to mixed radicals

Converting radicals to entire radicals

8.EE.A.3

Scientific notation

8.EE.B.5

Parallel and perpendicular lines in linear functions

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Identifying proportional relationships

8.EE.B.6

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>

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

8.EE.C.7

Introduction to linear equations

Model and solve one-step linear equations: ax = b, x/a = b

One-step Linear Equations

One Step Linear Equations — Word Problem

One-step equations

One-step Equations LHS

One-step Equations RHS

Model And Solve One Step Linear Equations Divide – Word Problem

Model And Solve One Step Linear Equations Multiply – Word Problem

Solving two-step linear equations using addition and subtraction: ax + b = c

Two-step Linear Equations

Two-step Linear Equations LHS

Solve Linear Equations Using Addition and Subtraction – Word Problem

Two-step Linear Equations — Word Problem

Solving two-step linear equations using multiplication and division: x/a + b = c

Two-step Linear Equations RHS

Solving two-step linear equations using distributive property: a(x + b) = c

Solve Linear Equations Using Distributive Property – Word Problem

Solving literal equations

8.EE.C.8

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

8.F.A.1

Relationship between two variables

Identifying functions

8.F.A.2

Function notation

8.F.B.4

Applications of linear relations

8.F.B.5

Graphing linear functions using table of values

8.G.A.1

Line symmetry

Tessellations using translations and reflections

tessellations using translations and reflections

8.G.A.2

Rotational symmetry and transformations

8.G.A.3

Enlargements and reductions with scale factors

Tessellations using rotations

8.G.A.4

Similar polygons

8.G.A.5

Similar triangles

8.G.B.6

Pythagorean theorem

Pythagorean Theorem

8.G.B.7

Using the pythagorean relationship

8.G.B.8

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

Applications of pythagorean theorem

8.G.C.9

Volume of cylinders

Word problems relating volume of prisms and cylinders

Surface area and volume of cones

Surface area and volume of spheres

8.NS.A.1

Understanding the number systems

Rational vs. Irrational numbers

8.NS.A.2

Determine square roots of rational numbers

Square roots of rational numbers

Estimating square roots

Converting repeating decimals to fractions

8.SP.A.1

Reading linear relation graphs

Box-and-whisker plots and scatter plots

8.SP.A.2

Solving linear equations by graphing

8th Grade Math

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

Evaluating and simplifying radicals