Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3

Maharashtra State Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3

Question 1.
State the order of the surds given below.
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 1
Answer:
i. 3, ii. 2, iii. 4, iv. 2, v. 3

Question 2.
State which of the following are surds Justify. [2 Marks each]
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 2
Answer:
i. \(\sqrt [ 3 ]{ 51 }\) is a surd because 51 is a positive rational number, 3 is a positive integer greater than 1 and \(\sqrt [ 3 ]{ 51 }\) is irrational.

ii. \(\sqrt [ 4 ]{ 16 }\) is not a surd because
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 3
= 2, which is not an irrational number.

iii. \(\sqrt [ 5 ]{ 81 }\) is a surd because 81 is a positive rational number, 5 is a positive integer greater than 1 and \(\sqrt [ 5 ]{ 81 }\) is irrational.

iv. \(\sqrt { 256 }\) is not a surd because
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 4
= 16, which is not an irrational number.

v. \(\sqrt [ 3 ]{ 64 }\) is not a surd because
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 5
= 4, which is not an irrational number.

vi. \(\sqrt { \frac { 22 }{ 7 } }\) is a surd because \(\frac { 22 }{ 7 }\) is a positive rational number, 2 is a positive integer greater than 1 and \(\sqrt { \frac { 22 }{ 7 } }\) is irrational.

Question 3.
Classify the given pair of surds into like surds and unlike surds. [2 Marks each]
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 6
Solution:
If the order of the surds and the radicands are same, then the surds are like surds.

Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 7
Here, the order of 2\(\sqrt { 13 }\) and 5\(\sqrt { 13 }\) is same and their radicands are also same.
∴ \(\sqrt { 52 }\) and 5\(\sqrt { 13 }\) are like surds.

Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 8
Here, the order of 2\(\sqrt { 17 }\) and 5\(\sqrt { 3 }\) is same but their radicands are not.
∴ \(\sqrt { 68 }\) and 5\(\sqrt { 3 }\) are unlike surds.

Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 9
Here, the order of 12\(\sqrt { 2 }\) and 7\(\sqrt { 2 }\) is same and their radicands are also same.
∴ 4\(\sqrt { 18 }\) and 7\(\sqrt { 2 }\) are like surds.

Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 10
Here, the order of 38\(\sqrt { 3 }\) and 6\(\sqrt { 3 }\) is same and their radicands are also same.
∴ 19\(\sqrt { 12 }\) and 6\(\sqrt { 3 }\) are like surds.

v. 5\(\sqrt { 22 }\), 7\(\sqrt { 33 }\)
Here, the order of 5\(\sqrt { 22 }\) and 7\(\sqrt { 33 }\) is same but their radicands are not.
∴ 5\(\sqrt { 22 }\) and 7\(\sqrt { 33 }\) are unlike surds.

Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 11
Here, the order of 5√5 and 5√3 is same but their radicands are not.
∴ 5√5 and √75 are unlike surds.

Question 4.
Simplify the following surds.
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 12
Solution:
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 13

Question 5.
Compare the following pair of surds.
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 14
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 15
Solution:
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 16
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 17

Question 6.
Simplify.
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 18
Solution:
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 19

Question 7.
Multiply and write the answer in the simplest form.
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 20
Solution:
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 21

Question 8.
Divide and write form.
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 22
Solution:
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 23

Question 9.
Rationalize the denominator.
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 24
Solution:
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 25
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 26

Question 1.
\(\sqrt { 9+16 }\) ? + \(\sqrt { 9 }\) + \(\sqrt { 16 }\) (Texbookpg. no. 28)
Solution:
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 27

Question 2.
\(\sqrt { 100+36 }\) ? \(\sqrt { 100 }\) + \(\sqrt { 36 }\) (Textbook pg. no. 28)
Solution:
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 28

Question 3.
Follow the arrows and complete the chart by doing the operations given. (Textbook pg. no. 34)
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 29
Solution:
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 30

Question 4.
There are some real numbers written on a card sheet. Use these numbers and construct two examples each of addition, subtraction, multiplication and division. Solve these examples. (Textbook pg. no. 34)
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 31
Solution:
Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.3 32

Maharashtra Board Class 9 Maths Solutions

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