Radical Expressions Review

Simplify Exponents

100

x⁵ • x⁷

What is x¹²

200

 (4x^2y)^3 

64x^6y^3

300

(6a² b)(−3ab³)

−18a³b⁴

400

(x² y² z^-1)³ (xyz⁴)(x^-3y)

x⁴y⁸z

500

 (2x^-2)/3 * 3^2(2^-4x)^2 

3/32

Simplify Radical Expressions

100

sqrt(49)

7

200

 8 sqrt(12) 

16 sqrt(3)

300

 sqrt(103x^4 

x^2sqrt(103)

400

sqrt(45y^2) 

3ysqrt5

500

 sqrt(1000x^3) 

10xsqrt(10x)

+/- Radical Expressions

100

 3sqrt 2 + 9 sqrt 2 

12sqrt 2

200

 6sqrt 3+sqrt 5-8sqrt 3+9sqrt 5 

-2sqrt3+10sqrt5

300

 8sqrt3-sqrt12+3sqrt3 

9sqrt3

400

 sqrt18+sqrt8+sqrt32 

9sqrt2

500

 sqrt117-sqrt52 

What is 

sqrt13

Mult/Div Radical Expressions

100

 3sqrt8*2sqrt6 

24sqrt3

200

 3sqrt(5a)*2asqrt(5a)  

30a^2

300

 (16sqrt(108))/sqrt3 

96

400

 (sqrt125 - sqrt27)/15 

1/3sqrt5-1/5sqrt3

500

  (sqrt125 - sqrt27)/(15sqrt15) 

sqrt3/9- sqrt5/25

Pythag, Distance, Midpoint

100

The third side of a right triangle if the hypotenuse is 15 inches and one leg is 9 inches.

What is 12 inches?

200

The distance between the points (6, 5) and (1, -7).

What is 13?

300

The distance between (4, 0) and (-6, 12)

What is  4sqrt61? 

400

The midpoint of the segment (7, 5) and (-12, 9)..

What is  (-5/2, 7)? 

500

The midpoint of the segment (4, 5) and (2, 3) and proof that it is the midpoint.

What is (3, 4)? The distance between (4,5) and (3, 4) is  sqrt 2  and the distance between (3,4) and (2,3) is  sqrt2 so they are equal. (or the distance between (4,5) and (2,3) is  2sqrt2