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Master Square Root Estimation: Quick & Accurate Techniques

NY.GEO-G.C.1

Central angles and proofs

NY.GEO-G.C.2a

Central and inscribed angles in circles

NY.GEO-G.C.2b

NY.GEO-G.C.5

auto-gen

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

NY.GEO-G.CO.1

Line symmetry

Angles in a circle

Chord properties

Circles and circumference

Circle properties

Arcs of a circle

Areas and sectors of circles

Parallel and perpendicular line segments

Identifying Parallel Lines

Identifying Perpendicular Lines

NY.GEO-G.CO.10

Classifying triangles

Isosceles and equilateral triangles

NY.GEO-G.CO.11

Area and perimeter of parallelograms

2d shapes area and perimeter of parallelogram

2d shapes area and perimeter of parallelograms

NY.GEO-G.CO.12

Perpendicular bisectors

NY.GEO-G.CO.13

Inscribed angles and proofs

NY.GEO-G.CO.2

Rotational symmetry and transformations

Introduction to transformations

NY.GEO-G.CO.3

Horizontal and vertical distances

NY.GEO-G.CO.6

Congruence and congruent triangles

NY.GEO-G.CO.7

Triangles congruent by SSS proofs

NY.GEO-G.CO.8

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

NY.GEO-G.CO.9

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

NY.GEO-G.GMD.1

Surface area and volume of prisms

Surface area and volume of cylinders

Surface area and volume of cones

NY.GEO-G.GMD.3

Surface area and volume of pyramids

NY.GEO-G.GMD.4

Surface area of 3-dimensional shapes

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

NY.GEO-G.GPE.1a

Conics - Circle

NY.GEO-G.GPE.1b

NY.GEO-G.GPE.4

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

General form:  Ax  + By  + C = 0

General form: Ax + By + C = 0

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

Introduction to vectors

NY.GEO-G.GPE.5

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

NY.GEO-G.GPE.6

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>

NY.GEO-G.GPE.7

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

NY.GEO-G.MG.1

Scale diagrams

NY.GEO-G.MG.2

Word problems of polynomials

NY.GEO-G.SRT.1

Enlargements and reductions with scale factors

NY.GEO-G.SRT.2

Similar triangles

NY.GEO-G.SRT.4

Pythagorean theorem

Pythagorean Theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

NY.GEO-G.SRT.5

Similar polygons

NY.GEO-G.SRT.6

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

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

NY.GEO-G.SRT.7

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

Cofunction identities

NY.GEO-G.SRT.8

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

NY.GEO-G.SRT.9

Area of triangles: 1/2 a*b sin(C)

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