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Question 1. Find the value of  
32 48
812
+
+
Solution:
Since 32 16 2 =× = 42; 48 16 3 4 3 =×=
8 = 42 × = 
22and 12 4 3 2 3 =× =
?  
32 48
812
+
+
 = 
42 4 3
22 2 3
+
+
 = 
()
()
42 3
2
22 3
+
=
+
Question 2. If  
2
 = 1.4142 then find the value 
– 21
21 +
.
Solution: Rationalising the denominator of 
2–1
21 +
, we get
2–1
21 +
=
2–1 2–1
21 2–1
×
+
 = 
()
()
()
2
2
2
2–1
2–1
=
()
2
2–1
2–1
 = ()
2
2–1
?  
2–1
21 +
=
()
2
2–1 or  
2–1
21 +
 =  
2–1
........ (1)
ä   
2
= 1.4142
â  
2–1
21 +
=
2–1
= 1.4142 – 1 = 0.4142
Question 3. Find the value of 'a' in 
–
–
35 19
a5
32 5 11
=
+
Solution:
L.H.S. =
3– 5
32 5 +
=
3– 5
32 5 +
 × 
3– 2 5
3–2 5
Rationalising the
denominator
 
=
()
()
2
2
9–6 5 –3 5 10
3–25
+
     
22
using (a b) (a – b) a – b +=
=
19 – 9 5 19 – 9 5
9 – 20 –11
= = 
919
5–
11 11
R.H.S. =
19
5–
11
a
since,  L.H.S. =  R.H.S.
Page 2


  
Question 1. Find the value of  
32 48
812
+
+
Solution:
Since 32 16 2 =× = 42; 48 16 3 4 3 =×=
8 = 42 × = 
22and 12 4 3 2 3 =× =
?  
32 48
812
+
+
 = 
42 4 3
22 2 3
+
+
 = 
()
()
42 3
2
22 3
+
=
+
Question 2. If  
2
 = 1.4142 then find the value 
– 21
21 +
.
Solution: Rationalising the denominator of 
2–1
21 +
, we get
2–1
21 +
=
2–1 2–1
21 2–1
×
+
 = 
()
()
()
2
2
2
2–1
2–1
=
()
2
2–1
2–1
 = ()
2
2–1
?  
2–1
21 +
=
()
2
2–1 or  
2–1
21 +
 =  
2–1
........ (1)
ä   
2
= 1.4142
â  
2–1
21 +
=
2–1
= 1.4142 – 1 = 0.4142
Question 3. Find the value of 'a' in 
–
–
35 19
a5
32 5 11
=
+
Solution:
L.H.S. =
3– 5
32 5 +
=
3– 5
32 5 +
 × 
3– 2 5
3–2 5
Rationalising the
denominator
 
=
()
()
2
2
9–6 5 –3 5 10
3–25
+
     
22
using (a b) (a – b) a – b +=
=
19 – 9 5 19 – 9 5
9 – 20 –11
= = 
919
5–
11 11
R.H.S. =
19
5–
11
a
since,  L.H.S. =  R.H.S.
  
i.e. 
919
5–
11 11
  =  
19
5–
11
a
  ?
9
 
11
= a
Question 4. Find the value of 'a' and 'b'
 
75 7–5
–
7– 5 7 5
+
+
 =  
7
a5b
11
+
Solution:
L.H.S. = 
75 7–5
–
7– 5 7 5
+
+
=   
()()
()()
22
75 –7–5
7– 5 7 5
+
+
=
49 514 5–49–514 5
49 – 5
++ +
= 
47 5
75
44 11
??
??
=
=
7
05
11
+
R.H.S. =  a + 
7
5b
11
Since, L.H.S. = R.H.S
? 0 + 
7
5
11
 =  a + 
7
5b
11
? a = 0 and b = 1
Question 5. If  a = 
35
2
+
, then find the value of +
2
2
1
a
a
.
Solution:  a = 
35
2
+
 ?  
1
a
 =  
2
35 +
Now  
2
2
1
+ a
a
 = 
2
1
–2
??
+
??
??
a
a
? 
2
2
1
+ a
a
=
2
35 2
–2
23 5
??
+
+
??
+
??
 = 
()
()
2
2
2
35 2
–2
23 5
??
++
??
??
+
??
??
=
2
95 2 3 5 4
–2
23 2 5
??
++ × × +
??
×+
??
=
2
18 6 5
–2
62 5
??
+
??
+
??
=
()
()
2
63 5
–2
23 5
??
+
??
??
+
??
=
2
6
–2
2
??
??
??
= ()
2
3–2
=9 – 2 = 7
So, 
2
2
1
+ a
a
= 7
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1 videos|228 docs|21 tests

FAQs on Higher Order Thinking Skills - Number System - Extra Documents & Tests for Class 9

1. What are higher order thinking skills?
Ans. Higher order thinking skills refer to the cognitive abilities that go beyond basic memorization and comprehension. These skills include critical thinking, problem-solving, analysis, synthesis, evaluation, and creativity. They require students to think deeply, apply knowledge, analyze information, and make connections.
2. How do higher order thinking skills benefit students?
Ans. Higher order thinking skills are essential for students as they promote critical thinking and problem-solving abilities. These skills help students to analyze information, make connections, think creatively, and apply knowledge in real-life situations. Developing these skills enables students to become active learners, independent thinkers, and effective problem solvers.
3. How can teachers promote higher order thinking skills in the classroom?
Ans. Teachers can promote higher order thinking skills in the classroom by incorporating activities and strategies that require students to think critically and analytically. Some methods include asking open-ended questions, encouraging discussions and debates, providing opportunities for problem-solving and project-based learning, and promoting reflection and self-assessment.
4. What is the role of higher order thinking skills in the number system?
Ans. Higher order thinking skills play a crucial role in understanding and applying concepts in the number system. For example, when working with complex number operations or solving word problems, students need to analyze the problem, think critically to choose the appropriate method, and apply their knowledge of number system operations to solve the problem accurately.
5. How can students develop higher order thinking skills in the number system?
Ans. Students can develop higher order thinking skills in the number system by practicing problem-solving activities that require critical thinking and analysis. They can also engage in discussions and collaborative tasks that encourage them to explain their thinking processes and justify their solutions. Additionally, using real-life examples and relating number system concepts to everyday situations can help students apply their knowledge and develop higher order thinking skills.
1 videos|228 docs|21 tests
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