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NUMBER SYSTEM AND EQUATIoNS L3 - surd

Total questions: 20

Worksheet time: 40mins

Name
Class
Date
1.

Rationalise its denominator

a)
b)
c)
d)
2.

 63\sqrt{63}  

a)

 63\sqrt{63}  

b)

 737\sqrt{3}  

c)

 373\sqrt{7}  

d)

 3173\sqrt{17}  

3.

 (s1)(1+s)\left(\sqrt{s}-1\right)\left(1+\sqrt{s}\right)  

a)

 (s1)\left(s-1\right)  

b)

 (1s)\left(1-s\right)  

c)

 (s2 1)\left(s^{2\ }-1\right)  

d)

 (1s2)\left(1-s^2\right)  

4.

 (24)(2+4)\left(\sqrt{2}-4\right)\left(\sqrt{2}+4\right)  

a)

14

b)

 14-14  

c)

2

d)

 2-2  

5.

 (31)(3+1)\left(\sqrt{3}-\sqrt{1}\right)\left(\sqrt{3}+\sqrt{1}\right)  

a)

 2-2  

b)

2

c)

 4-4  

d)

4

6.

 (x2)(2+x)\left(x-\sqrt{2}\right)\left(\sqrt{2}+x\right)  

a)

 (2x)\left(2-x\right)  

b)

 (x2)\left(x-2\right)  

c)

 (x22)\left(x^2-2\right)  

d)

 (2x2)\left(2-x^2\right)  

7.

Permudahkan  2752\sqrt{75} 

a)

 10310\sqrt{3}  

b)

 150\sqrt{150}  

c)

 300\sqrt{300}  

d)

 50350\sqrt{3}  

8.
Simplify fully: 
√32 + 5√32
a)
6√32
b)
24√8
c)
24√2
d)
6√8
9.
Simplify fully: 
2√45 - 5√45 + 9√16
a)
-9√5 + 36
b)
-3√45 + 144
c)
6√16
d)
6√106
10.

What should you multiply 615\frac{6}{1-\sqrt{5}}  by to rationalize the denominator?

a)

-4

b)

 151-\sqrt{5}  

c)

 1+51+\sqrt{5}  

d)

 (335)2-\frac{\left(3-3\sqrt{5}\right)}{2}  

11.

What is a surd?

a)

A recurring decimal

b)

An irrational number

c)

A fraction

d)

A rational number

12.

Select a surd.

a)

√2

b)

√4

c)

√99

d)

√20

13.

Which of the following is NOT a surd?

a)

 3\sqrt{3}  

b)

 4\sqrt{4}  

c)

 5\sqrt{5}  

d)

 424\sqrt{2}  

14.

Choose the correct statements.

a)

57=12\sqrt{5}\sqrt{7}=\sqrt{12}

b)

32×22=623\sqrt{2}\times2\sqrt{2}=6\sqrt{2}

c)

4824=22\frac{4\sqrt{8}}{2\sqrt{4}}=2\sqrt{2}

d)

260=265\sqrt{260}=2\sqrt{65}

15.

Solve the radical equation. Don't forget to check your answers!

a)

No solution

b)

33

c)

61

d)

47

16.
Solve
a)
20
b)
-4
c)
4
d)
-10
17.
a)

12

b)

4

c)

16

d)

32

18.

Solve the radical equation: 11=2+90x11=2+\sqrt{90-x} 

a)

x = 9

b)

x = 82

c)

x = -9

d)

x = -82

19.

Solve the radical equation: x5=23x\sqrt{x-5}=\sqrt{23-x} 

a)

x = -14

b)

x = 14

c)

No Solution

d)

x = 28

20.

 (1636)2=576\left(\sqrt{16}\sqrt{36}\right)^2=576  

a)

Ya

b)

Tidak