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Finding the square and square root of a number

8.EE.A.1

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

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

sample

math

Ex. 1:

Ex. 2:

Square root of 225 with positive, negative, and no solution cases

- Hi, welcome to this question here. We're here trying to find out the root of 64. If you have a calculator, of course you can always just punch in it and get the answer. But let's say what if you don't. Now, if you do remember your perfect squared numbers, the root of 64 is just eight. Because, eight times eight does give you 64. But let's say you don't remember any perfect numbers, how do we do this from scratch? 
What you do is you find out all the prime factors of 64. So, let's go ahead and do that. There's a two right here and that's a 32, and divided by two I get a 16, divided by two which is just eight, divided by two goes four and here's my two and two, okay? 
So, imagine that the question now becomes two times the two times the two times the two times the two and I believe there's six times here. So, the real 64 is now just square root of two, two, two, two, two, two, all multiplied together, okay? 
So, how do we figure this out? Now, do you remember this is just a square root? There is actually a tiny little two here, that means the square root, right? The trick is you can pick any pair because you can only pick two, because it's a square root. That little number right here means that you can pick two identical numbers and just bring them out of the radical side. So, you can pick another one, you can pick another one. This one comes out, this one comes out and this one comes out so, the answer is just going to be a two here from the first one, and a two here from the second one, and a two here from the third one. The answer is just going to be two times two is four, four times two is eight. Which is exactly the same as what you have on the beginning, okay? 
So, this is the most, I guess, all the work that you can show for your homework. But if you do know the perfect square numbers, it'll be much easier, okay? 
Thanks for watching.

Finding the square root of 64 using prime factorization

Finding the negative square root of 676 using prime factorization

Why the square root of a negative number has no solution

To square is to raise the number to the second power. In other words, to square is to multiply the number by itself. Square root is the inverse operation of squaring. To square root is to find the two identical factors of a number.

Squares and Square Roots

Prime factorization