Adding and Subtracting Radicals
Simplifying Radicals
Multiplying and Dividing Radicals
Rationalization and Conjugation
Applications of Radicals
100

Subtract 

5 sqrt (3)

from

sqrt (3)

-4 sqrt 3

100

sqrt (18x^7y^9)

3x^3y^4sqrt(2xy)

100

Write your answer in simplified radical form.

5sqrt (2) * 7sqrt(2) *4sqrt(2). 

280 sqrt (2)

100

sqrt (1) / sqrt (6)

sqrt (6) / 6

100

Find the area of the square whose side measures

3sqrt(5).

45 square units

200

sqrt 8 + 3 sqrt 2 -4sqrt2

sqrt 2

200

sqrt (75a^3bc^8)

5ac^4sqrt(3ab)

200

sqrt (4ab) * sqrt (5b)

2b sqrt(5a)

200

(3 sqrt 4)/sqrt (32)

(3 sqrt 2)/4

200

Find the distance between (3, -5 ) and (-1, -9).

4 sqrt (2)  units

300

sqrt5 + sqrt (20) -sqrt (72)

3sqrt5 -6sqrt2

300

root(3)(3/16)

root(3)12/4

300

4 sqrt (8a^5c^7) * sqrt(6a^4c)

16a^4c^4sqrt(3a)

300

(sqrt(8x^4y^3))/(sqrt(14x^3y^5)

(2sqrt(7x))/(7y)

300

A picture frame measures 3√3 centimeters on one side. Answer the following questions:

1) Is the area a real number?

2.) Is the area perfect square?

3.) Is the area a rational or irrational number?


1.) Yes, a real number. 

2.) Not a perfect square

3.) Rational Number


400

asqrt 3-3asqrt3+sqrt2

-2asqrt3+sqrt2

400

(sqrt(5) - 2sqrt(3))^2

17 - 4sqrt(15)

400

Divide: 

sqrt ((72x^4y^3)/16)

(3x^2ysqrt (2y) )/ 2

400

2/(sqrt(3) + sqrt(5))

sqrt(5) - sqrt(3)

400

The legs of a right triangle are 10 cm and √3 cm. Find the hypotenuse. Express your answer in simplified radical form. 

sqrt 103  cm

500

sqrt (x^2/16) +sqrt (x^2/9)

(7x)/12

500

(sqrt(2tx^2z^3)*(sqrt(7txz^2)))/sqrt(10t^3x^2)

(z^2sqrt(35txz))/(5t)

500

What is the quotient of

sqrt (192pq) and sqrt(3q)?

8sqrt (p)

500

(1 + sqrt(2))/(sqrt(5) - sqrt(6))

-sqrt(5)-sqrt(6)-sqrt(10)-2sqrt(3)

500

Shan and Lily start from the same point. Shan walks 400 meters west. Lily walks x meters South until they are 600 meters apart. How far does Lily walk Approximate your answer to the nearest hundredths. 

447.21 meters