Scroll:Real number system >> Rationalization of surds >> ps (4191)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.


 

1)  

 Simplify by Rationalizing the denominator 

√ 5 +1
=
 		3+√ 5 
√ 5 -1


Answer:_______________




2)  

Rationalize the denominator of the following

2√ 7 
=
 		2√ 77 
√ 11 


Answer:_______________




3)  

Rationalize the denominator of the following

2
=
 		2√ 3 
3√ 3 


Answer:_______________




4)  

Rationalize the denominator of the following

1
=
 		√ 3 
√ 12 


Answer:_______________




5)  

 Simplify by Rationalizing the denominator 

1
=
 		11-√ 3 
11+√ 3 


Answer:_______________




6)  

Rationalize the denominator of the following

3
=
 		3√ 5 
√ 5 


Answer:_______________




7)  

Rationalize the denominator of the following

33√ 5 
=
 
3√ 9 


Answer:_______________




8)  

 Simplify by Rationalizing the denominator 

1
=
 		3-√ 5 
9+3√ 5 


Answer:_______________




9)  

 Simplify by Rationalizing the denominator 

√ 5 +1
=
 		3+√ 5 
√ 5 -1


Answer:_______________




10)  

Rationalize the denominator of the following

2√ 7 
=
 		2√ 77 
√ 11 


Answer:_______________




 

1)  

 Simplify by Rationalizing the denominator 

√ 5 +1
=
 		3+√ 5 
√ 5 -1 Answer: 2


SOLUTION 1 :

 

√ 5 +1
=
 		√ 5 +1
x
 		√ 5 +1
=
 		(√ 5 +1)2
√ 5 -1√ 5 -1√ 5 +1(√ 5 )2-12

 [ multiply & divide by conjugate of denominator ]

(√ 5 )2+2√ 5 .1+12
=
 		5+2√ 5 +1
=
 		 6+2√ 5 
=
 		2[3+√ 5 ]
=
 		3+√ 5 
5-1444 22

 

 



2)  

Rationalize the denominator of the following

2√ 7 
=
 		2√ 77 
√ 11  Answer: 11


SOLUTION 1 :

 

2√ 7 
=
 		2√ 7 
x
 		√ 11 
=
 		2√  7x112√ 77 
3√ 11 √ 11 √ 11 1111

 



3)  

Rationalize the denominator of the following

2
=
 		2√ 3 
3√ 3  Answer: 9


SOLUTION 1 :

 

2
=
 		2
x
 		  √ 3 
=
 		2√ 3 
=
 		2√ 3 
3√ 3 3√ 3 √ 3 3x39

 



4)  

Rationalize the denominator of the following

1
=
 		√ 3 
√ 12  Answer: 6


SOLUTION 1 :

 

1
=
 		1
x
 		√ 12 
=
 		√ 12 
=
 
=
 		2√ 3 
=
 		√ 3 
√ 12 √ 12 √ 12 126126

 



5)  

 Simplify by Rationalizing the denominator 

1
=
 		11-√ 3 
11+√ 3  Answer: 118


SOLUTION 1 :

 

1
=
 		 1
x
 		11-√ 3 
11+√ 3 11+√ 3 11-√ 3  

 [ multiply & divide by conjugate of denominator ]

11-√ 3 
=
 		 11-√ 3 
x
 		11-√ 3 
112-(√ 3 )2121-3118 

 

 



6)  

Rationalize the denominator of the following

3
=
 		3√ 5 
√ 5  Answer: 5


SOLUTION 1 :

 

3
=
 		3
x
 		√ 5 
=
 		3√ 5 
√ 5 √ 5 √ 5 5


7)  

Rationalize the denominator of the following

33√ 5 
=
 
Answer: √ 15 
3√ 9 


SOLUTION 1 :

 

33√ 5 
=
 		33√ 5 
x
 		3√ 9 
=
 		33√ 45 
3√ 9 3√ 9 3√ 9 3√ 81 

 

33√  15x3
=
 		33√ 15 3√ 3 
=
 		33√ 15 
=
 		33√ 15 
3√  27x33√ 27 3√ 3 33√  3x3x33

 

= 3√ 15 



8)  

 Simplify by Rationalizing the denominator 

1
=
 		3-√ 5 
9+3√ 5  Answer: 12


SOLUTION 1 :

 

1
=
 		1
x
 		9-3√ 5 9-3√ 5 
9+3√ 5 9+3√ 5 9-3√ 5 92-(3√ 5 )2

 [ multiply & divide by conjugate of denominator ]

9-3√ 5 
=
 		3[3-√ 5 ]3-√ 5 
81-4536 1212

 

 



9)  

 Simplify by Rationalizing the denominator 

√ 5 +1
=
 		3+√ 5 
√ 5 -1 Answer: 2


SOLUTION 1 :

 

√ 5 +1
=
 		√ 5 +1
x
 		√ 5 +1
=
 		(√ 5 +1)2
√ 5 -1√ 5 -1√ 5 +1(√ 5 )2-12

 [ multiply & divide by conjugate of denominator ]

(√ 5 )2+2√ 5 .1+12
=
 		5+2√ 5 +1
=
 		 6+2√ 5 
=
 		2[3+√ 5 ]
=
 		3+√ 5 
5-1444 22

 

 



10)  

Rationalize the denominator of the following

2√ 7 
=
 		2√ 77 
√ 11  Answer: 11


SOLUTION 1 :

 

2√ 7 
=
 		2√ 7 
x
 		√ 11 
=
 		2√  7x112√ 77 
3√ 11 √ 11 √ 11 1111