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Master Square Root Estimation: Quick & Accurate Techniques

TX.G.10.A

Surface area of 3-dimensional shapes

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

TX.G.10.B

auto-gen

Upper and lower bound

Upper and Lower Bound

TX.G.11.B

Areas and sectors of circles

TX.G.11.C

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

TX.G.11.D

Introduction to volume

Calculate the Volume

TX.G.12.A

Angles in a circle

Chord properties

Tangent properties

Circles and circumference

Circle properties

Central angles and proofs

Inscribed angles and proofs

Central and inscribed angles in circles

TX.G.12.B

Arcs of a circle

Circle chord, tangent, and inscribed angles proofs

TX.G.12.D

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

TX.G.12.E

Conics - Circle

TX.G.13.A

Permutations

Combinations

Problems involving both permutations and combinations

TX.G.13.B

Probability

TX.G.13.C

Probability of independent events

Addition rule for 

Addition Rule for "OR"

Addition rule for "OR"

Multiplication rule for 

Multiplication rule for "AND"

Multiplication Rule for "AND"

TX.G.13.D

Conditional probability

Probability with Venn diagrams

TX.G.13.E

Determining probabilities using tree diagrams and tables

Probability involving permutations and combinations

TX.G.2.A

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>

TX.G.2.B

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

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 and perpendicular lines in linear functions

TX.G.2.C

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

TX.G.3.A

Rotational symmetry and transformations

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

TX.G.3.B

Combining transformations of functions

Enlargements and reductions with scale factors

TX.G.3.C

Scale diagrams

TX.G.3.D

Line symmetry

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

TX.G.4.A

Inductive reasoning

Deductive reasoning

TX.G.4.B

Conditionals

Inverses, converses, and contrapositives

Biconditionals

TX.G.4.D

Algebraic proofs

TX.G.5.A

Congruence and congruent triangles

Pairs of lines and angles

Parallel lines and transversals

Perpendicular line proofs

TX.G.5.D

Classifying triangles

TX.G.6.A

Isosceles and equilateral triangles

Parallel line proofs

TX.G.6.B

Triangles congruent by SSS proofs

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

TX.G.6.D

Combination of SohCahToa questions

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

TX.G.6.E

Classifying quadrilaterals

Classifying Quadrilaterals

Word Problem: Classifying Quadrilaterals

TX.G.7.A

Similar triangles

Similar polygons

TX.G.8.B

Estimating square roots

TX.G.9.A

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)

TX.G.9.B

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Circles

Coordinate and transformational geometry

Logical argument and constructions

Proof and congruence

Two-dimensional and three-dimensional figures

math

Intro

- [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.

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