Unit 7 Review: Radicals

Rewrite Radicals

100

Convert the following expression to Exponential Form

sqrt(x)

x^(1/2)

200

Convert the following expression to Radical Form

f^(6/7)

root(7)(f^6)

300

Convert the following expression to Radical Form

(3k)^(4/5)

root(5)(3^4k^4)

400

Convert the following expression to Exponential Form

(sqrt(6x))^3

6^(3/2)x^(3/2)

500

Convert the following expression to Exponential Form

root(3)(27a^6b^9c^7)

3a^(2)b^3c^(7/3)

Simplify Radicals

100

Simplify the following radical:

sqrt(144)

sqrt(12)

200

Simplify the following radical:

sqrt(72)

6sqrt(2)

300

Simplify the following radical:

sqrt(90b^2)

3bsqrt(10)

400

Simplify the following radicals:

-2sqrt(72)-3sqrt(24)+2sqrt(128)

4sqrt(2)-6sqrt(6)

500

Simplify the following radical:

2sqrt(72x^4y^3)

12x^2ysqrt(2x)

+ - x ÷ Radicals

100

sqrt(2)+sqrt(2)

2sqrt(2)

200

sqrt(6)*2sqrt(3)

6sqrt(2)

300

sqrt(18)*sqrt(12)

6sqrt(6)

400

sqrt(3)+sqrt(12)-sqrt(27)

0

500

(sqrt(3))/(1+sqrt(2))

-(sqrt(3)+3)/2

Solving Radic

100

sqrt (4x) = 10

x = 25

200

8sqrt(3x)=48

x = 12

300

5sqrt((4x-8)/2) = 30

x = 20

400

sqrt(x/10) = sqrt(3x-58)

x = 20

500

x+4=sqrt(x+10)

x = -6 or x = -1

Radical Trivia

100

A whole number that has a whole number as its square root is called...

sqrt0,sqrt1,sqrt4,sqrt9,sqrt16,...

Perfect Squares

200

Square Root Day was May 5th, 2025.

When will the next Square Root Day be?

June 6th, 2036 or 6/6/36

300

If a square has side length 1, what is the length of its diagonal?

sqrt2

400

What does the radical symbol √ come from?

(Hint: Latin Roots)

The Latin word radix, meaning “root.”

500

What civilization approximated √2 over 3,000 years ago, and whose estimate was accurate to several decimal places.

The Ancient Babylonians