Radical, Rational and Irrational Operations

Vocabulary

100

A number that can be written as a fraction

Rational

200

A number that cannot be expressed as a fraction

Irrational

300

A value that produces a whole number when square rooted. 

Perfect Square

400

The number or expression inside the radical

Radicand

500

The little number outside the radical letting you know if its a square root, cube root, etc

Index

Simplify Radicals

100

sqrt(81)

9

200

sqrt(x²)

x

300

sqrt(27)

3sqrt(3)

400

cuberoot(8x⁴)

2xcuberoot(x)

500

cuberoot(320)

4cuberoot(5)

Radical Operations (Remember to Simplify)

100

sqrt(2)+3sqrt(2)

4sqrt(2)

200

4sqrt(5)+sqrt(500)

14sqrt(5)

300

sqrt(3)*sqrt(6)

3sqrt(2)

400

3cuberoot(4x²)*5cuberoot(6x)

30xcuberoot(3)

500

cuberoot(8b⁴)-2cuberoot(27b⁴)

-4bcuberoot(b)

Rational or Irrational? Include why.

100

sqrt(5)

irrational because it is an imperfect root

200

sqrt(4)+sqrt(3)

irrational because the sum of irrational numbers (sqrt3) with rational numbers (sqrt4) is irrational

300

pi/pi

rational because pi/pi=1 which is whole (pi by itself is irrational because the decimal continues forever without repeating)

400

sqrt(20)*sqrt(5)

rational because 20*5 is 100 which is a perfect square

500

sqrt(4)+cuberoot(9)*cuberoot(3)+5.323232...

rational because each part of the sum is rational (sqrt4=2, 9*3=27 --> cuberoot 27=3, and the decimal repeats)

Random and Unfair

100

What is x? 2x=x²

x=2

200

sqrt(1000000)

1000

300

What city and state is Mr. Fritsche in right now?

Minneapolis, Minnesota

400

What is a prime number?

A number whose only factors are 1 and itself. 

500

What school do you attend? (full name)

Susan Todd Pearson Middle School