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Master Square Root Estimation: Quick & Accurate Techniques

Demonstrate understanding of powers with integral bases and whole number exponents

Using exponents to describe numbers

Expanded powers

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Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Using exponents to solve problems

Demonstrate understanding of rational numbers by comparing and ordering rational numbers

Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Solving problems with rational numbers in decimal form

Mixed Operations with Decimals

Mixed Operations

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

Solving problems with rational numbers in fraction form

Operations with fractions

Explain and apply the order of operations including exponents with and without technology

Order of operations (PEMDAS)

Identify the Order of Operations

Order of Operations — Word Problem

Determine the square root of positive rational numbers that are perfect squares

Determine square roots of rational numbers

Square roots of rational numbers

Squares and square roots

Square Root of a Perfect Square

Determine the approximate square root of positive rational numbers that are non-perfect squares

Estimating square roots

Generalize a pattern arising from a problem-solving context using linear equations

Representing patterns in linear relations

Represent Patterns in Linear Relations Equation Decimal

Represent Patterns in Linear Relations Equation Integer Start From 0

Represent Patterns in Linear Relations Equation Integer Start From 1

Represent Patterns in Linear Relations Equation Negative Decimal

Identify the Linear Equation

Reading linear relation graphs

Solving linear equations by graphing

Graph linear relations analyze the graph and interpolate or extrapolate to solve problems

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Model and solve problems using linear equations of various forms

Solving linear equations using multiplication and division

Two-step Linear Equations LHS

Two-step Linear Equations RHS

Solving two-step linear equations: ax + b = c, x/a + b = c

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

Solving linear equations with variables on both sides

Solving literal equations

Explain and illustrate strategies to solve single variable linear inequalities

Compound inequalities

Analyze the Alternate Form of Compound Inequalities: AND

Compound linear inequalities

Evaluate Compound Inequalities: And

Express linear inequalities graphically and algebraically

Graph the Inequality

Linear Inequalities – Word Problem 

Linear inequalities

Solving one-step linear inequalities

One-step Linear Inequalities

One-step linear inequalities

One-step Linear Inequalities Decimal

One-step Linear Inequalities Decimal with Fraction

One-step Linear Inequalities Fraction

Solve One Step Linear Inequalities Find Solution– Word Problem

One-step Linear Inequalities — Word Problem

Solving multi-step linear inequalities

Multi-step Linear Inequalities

Two-step Linear Inequalities

Multi-step linear inequalities

Two-step linear inequalities

Solve Multi-step Linear Inequalities – Word Problem 

Solve Multi Step Linear Inequalities Solve Equation – Word Problem

Solve Multi Step Linear Inequalities Equation – Word Problem

Demonstrate an understanding of polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Model record and explain the operations of multiplication and division of polynomial expressions

Multiplying and dividing monomials

Divide a monomial by a monomial

Multiply a monomial by a monomial

Multiplying polynomials by monomials

Multiply a polynomial by a monomial

Dividing polynomials by monomials

Model and solve problems using 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

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

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

Solve Linear Equations Using Distributive Property – Word Problem

Describe the effect of various factors on the collection of data

Influencing factors in data collection

Data collection

Select and defend the choice of using either a population or a sample of a population

Sampling methods

Sampling Methods

Census and bias

Census and Bias

Classifying Bias

Develop and implement a project plan for the collection display and analysis of data

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Bivariate, scatter plots and correlation

Demonstrate an understanding of the role of probability in society

Probability

Solve problems and justify the solution strategy using circle properties

Angles in a circle

Chord properties

Tangent properties

Determine the surface area of composite 3-D objects to solve problems

Surface area of 3-dimensional shapes

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Surface area of cylinders

Demonstrate an understanding of similarity of polygons

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Demonstrate an understanding of line and rotation symmetry

Line symmetry

Rotational symmetry and transformations

Grade 9

Develop number sense

Use patterns to describe the world and solve problems

Represent algebraic expressions in multiple ways

Collect display and analyze data to solve problems

Use direct or indirect measurement to solve problems

math

Intro

Finding whole numbers with squares between 8 and 9

Estimating the square root of 24 using a number line

- [Instructor] Hi, welcome to this question right here. So we're trying to estimate what is root 66 manually, now without the calculator. So the work is actually pretty simple. You draw yourself a number line and you make yourself two lines right here to represent two numbers. Now these two numbers here is going to be enclosing the 66 but they have to be perfect square numbers. For example, 64 is... that's the first number that come to me because 66 is greater than 64, right? Sixty-four turns out to be and eight square which is a perfect square number. So I know the root 66 is definitely greater than eight but eight point something, something which I don't know yet. Then this number over here is going to be... after eight there's a nine, nine times nine is 81. So this is 81 right here. So I know this root 66 is definitely between 8 and the 9. But where is it? 
Well, we can actually calculate it approximately, estimation. Take the 81 right here and subtract to 64. There's 17 units across from 64 to 81. 17, so I'm not going to do all of them though. I'm just going to cut it in half. So this will be 8.5, and if there's 17 units. 17 divided by 2 I get 8.5 units. So 64 + 8.5, I got myself-- This is actually my 72.5, on the number line, but in terms of the square root of this number. Let me put square numbers on these guys right here. It will be 8.5, just perfectly halfway. Now, the 66 is actually between these two guys right here, but are they closer to the half or they're closer to the 8? 
Well, if I just take my 72.5 over here and subtract the 64, I have 8.5 units. So this one is actually not that bad. I can actually do 8.5, then I go-- That's halfway, that's 1, 2, 3, 4 5, 6, 7, 8 and a half maybe. This is approximation, so don't be too serious about these guys. Approximately 8.5 units. Okay, then I think-- Every unit is a one now, so that's 66 right? This is 64, 65, 66 is right here. This is my 66, okay? So that's root 64, root 65, root 66. So as you can see, it's very, very close to my 8. See, this is 8 right here. This is 8.5, so if you just quickly do a quick approximation. It will be 8.1, 8.2, 8.3 and 8.4. If I just quickly draw a lines approximately because I don't, I didn't really do have a good scale on these guys. If you have like a grid paper, probably much easier. This is 8 right? 
Then this is like 8.1, 8.2, 8.3, 8.4, 8.5. So it looks like I'm just a little bit on the 8.1 something. I'm going to do an approximation, 8.1. That's pretty much it, 8.10. That's what I'm going to put down. Approximately estimated, it's going to be my 8.10. Now, if I punch it in a calculator, radical of 66 then I got myself-- I'm pretty close actually. It's going to be 8.12, but once again I don't have a good scales right here. If you draw them perfectly with the equal distance, if you draw the units perfectly, you will get a better approximation than this. But that's the work, and once again find your perfect score numbers that will enclose that number 66, and then just draw, figure out how many units between them, figure out how many units between them, then just slowly figure out where your location is and just do the approximation. Thanks for watching.

Estimating the square root of 66 using a number line

Estimating the square root of 110 using perfect squares

Finding the side length of a square cake using square roots

Checking if the square cake fits inside the rectangular box

Understanding square roots and estimating non-perfect square roots

Using number lines to estimate square roots without a calculator

To estimate square roots which are not perfect squares without using a calculator, we need to know the perfect square numbers well. We will first put the number inside the square root sign in the middle of a number line, and then find the two closest perfect square numbers on its left and right hand side to make the best estimation.

How do you estimate the value of square roots?

Divisibility rules

Introduction to Exponents