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

Grade 10 Math: Master Essential Skills & Concepts

WA10.1

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Conversions between metric and imperial systems

Metric to Imperial Conversions

Imperial to Metric Conversions

Conversions Between Metric and Imperial Systems Speed KM to MI

Conversions Between Metric and Imperial Systems Speed  MI to M

Metric-Imperial Length Conversion Inch To Cm

Metric-Imperial Length Conversion MM/CM/M/KM To FT

Metric-Imperial Length Conversion MM/CM/M/KM To MI

Metric systems

Add and Subtract Mixed Units

Metric Length Conversion

Add or Subtract Different Metric Units Convert to CM

Add or Subtract Different Metric Units Convert to M

Add or Subtract Different Metric Units Convert to MM

Imperial systems

Imperial Length Conversion

Conversions involving squares and cubic

Imperial to Metric Conversions — Squares and Cubes

Imperial Conversion — Squares and Cubes

Metric to Imperial Conversion — Squares and Cubes

Metric Area Conversion FT to CM

Metric Area Conversion Foot to Inch

Metric Area Conversion M/CM to Inch

WA10.10

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

Find the difference of squares

Evaluating polynomials

Using algebra tiles to factor polynomials

Applications of polynomials

Common factors of polynomials

WA10.11

Solving polynomial equations

Word problems of polynomials

Factoring polynomials by grouping

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

WA10.2

Upper and lower bound

Upper and Lower Bound

WA10.3

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

WA10.4

Understanding the number systems

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

Rational vs. Irrational numbers

WA10.5

Evaluating and simplifying radicals

Converting repeating decimals to fractions

Square and square roots

Square Root of a Perfect Square

Cubic and cube roots

Cube root of a perfect cube

Converting radicals to mixed radicals

WA10.6

Product rule of exponents

Converting radicals to entire radicals

Adding and subtracting radicals

Adding radicals

Subtracting radicals

Multiplying and dividing radicals

Dividing radicals

Multiplying radicals

Rationalize the denominator

WA10.7

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Simplify the power

Solving for exponents

WA10.8

Negative exponent rule

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

What is a polynomial?

Classifying Polynomials

WA10.9

Polynomial components

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

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Workplace and Apprenticeship Mathematics 10

Number Sense, Logical Thinking, Mathematics as a Human Endeavour

math

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https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-grade10math.png

Ex. 1:

Intro

Simplifying the square root of 18 to a mixed radical

Simplifying sqrt(1088) using perfect squares and prime factorization

Simplifying -2√45 using perfect squares and prime factorization

<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>


Simplifying 7/11 times radical 1250 using prime factorization

Simplifying 3 times the fourth root of 162 to a mixed radical

Simplifying 2 times the 5th root of negative 192

Simplifying a square root with coefficient, prime number, and variables

Simplifying 2 times cube root of 250a^13 to a mixed radical

Simplifying radicals using prime factorization

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