Show:
Simplify Surds
Surds Properties
Matching Expressions
Surds in Context
Quick Questions
100

Simplify √ 18 

3√ 2

100

What is the property of √a x √b ?

√a x √b = √(ab)

100

Match √8 with its simplify form.
A. 2√2
B. 4√2
C. √8
D. √(2 x 4)

A. 2√2

100

If a square garden has an area of 50 square meters, what is the length of one side?

√50
= 5√2 meters

100

Simplify √45

3√5

200

Simplify √72

6√ 2

200

What is the property of √a / √b ?

√a / √b =√(a/b)

200

Match √50 with its simplified form.
A. 5√10
B. √(5 x 10)
C. 5√2
D. 10√5

C. 5√2

200

The diagonal of a square garden is √72 meters. What is the length of each side of the garden?

d = a√2
6√2 / √2
= 6 meters

200

What is √2 x √8 ?

√16 =4

300

Simplify √50

5√ 2

300

How do you simplify √a x √a ?

√a x √a = a

300

Match √18 with its simplified version.
A. √(6 x 3)
B. 2√3
C. √18
D. 3√2

D. 3√2

300

A right triangle has sides of length 4 meters and 3 meters. What is the length of the hypotenuse?

√(42+32) = √(16+9) =√ 25 =5 meters

300

Simplify √32 x √2

√64= 8

400

Simplify √200

10√ 2

400

Simplify (√3)2 

3

400

Match √98 with its simplified form.
A. 2√7
B. 7√2
C. √98
D. 2√69

B. 7√2

400

A garden is designed with dimensions 5√3 meters by 2√3 meters. What is the length of the diagonal of the garden?

d2 = (5√3)2 + (2√3)2
d2 = 75 + 87
d = √87 meters

400

Simplify √75 / √3

√25= 5

500

Simplify √98

7√2

500

What is √(a2) when a is positive?

a

500

Match √200 with its simplified form.
A. 5√100
B. 2√10
C. √(20 x 10)
D. 10√2 

D. 10√2 

500

You need to find the diagonal of a rectangular room with dimensions 7√2 meters by 5√2 meters. What is the length of the diagonal? 

d2 = (7√2)2 + (5√2)2
d2 = 98 +50
d = √148
d= 2√37 meters

500

Simplify √36a / √6a

= √(36a/6a)
=√6