Operations with Radicals

Vocabulary

100

What is the number under the radical symbol called?

Radicand

200

What is the number in the small dent of the radical symbol called?

Index

300

What is the inverse operation of squaring a number?

Square root

400

When can you simplify a radicand?

When it has a perfect square factor. 

500

When can you add and subtract radicals?

When the radicals contain the same radicand. 

SimplifyingRadicals

100

Simplify.

sqrt50

5sqrt2

200

Simplify. 

sqrt(450)

15sqrt2

300

Simplify. 

-5sqrt(27)

-15sqrt(3)

400

Simplify. 

sqrt(100/49)

10/7

500

Simplify. 

sqrt(48/9)

(4sqrt3)/3

AddingRadicals

100

Simplify:

5sqrt7+8sqrt7

13sqrt7

200

Simplify:

3sqrt5+4sqrt3+sqrt5

4sqrt5+4sqrt3

300

Simplify:

5sqrt2+sqrt8

7sqrt2

400

Simplify:

sqrt98+sqrt32

11sqrt2

500

Simplify: 

3sqrt75+4sqrt12

23sqrt3

SubtractingRadicals

100

Subtract.

sqrt6-6sqrt6

-5sqrt6

200

Subtract.

7sqrt3-4sqrt3-2sqrt3

sqrt3

300

Subtract.

sqrt(16/4)-sqrt25

-3

400

Subtract.

8sqrt8-sqrt200

6sqrt2

500

sqrt125-sqrt45-sqrt98-4sqrt8

2sqrt5-15sqrt2

MultiplyingRadicals

100

5sqrt2(4sqrt5)

 

20sqrt10

200

-3sqrt3(6sqrt6)

-54sqrt2

300

\(-3sqrt3)^2

27

400

(3sqrt(5))^2

45

500

3sqrt6(5sqrt3-sqrt2)

45sqrt2-6sqrt3

Combo

100

Simplify 2sqrt5*(sqrt6+2) 

2sqrt30+4sqrt5

200

Simplify 

sqrt(3)*(sqrt6+sqrt10)

3sqrt(2)+sqrt(30)

300

Simplify 

(sqrt5)(sqrt45+sqrt8)

15+2sqrt10

400

Simplify 

sqrt6(4sqrt12+5sqrt8)

24sqrt2+20sqrt3

500

Simplify

(4sqrt25)(4sqrt5-3sqrt4)

80sqrt5-120