# NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5.

• Number Systems Class 9 Ex 1.1
• Number Systems Class 9 Ex 1.2
• Number Systems Class 9 Ex 1.3
• Number Systems Class 9 Ex 1.4
• Number Systems Class 9 Ex 1.5
• Number Systems Class 9 Ex 1.6

## NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5

Ex 1.5 Class 9 Maths Question 1.
Classify the following numbers as rational or irrational:
(1) 2- $\sqrt { 5 }$
(2) (3+ $\sqrt { 23 }$ )- $\sqrt { 23 }$
(3) $\cfrac { 2\sqrt { 7 } }{ 7\sqrt { 7 } }$
(4) $\cfrac { 1 }{ \sqrt { 2 } }$
(5) 2π
Solution:
(1) Irrational ∵ 2 is a rational number and $\sqrt { 5 }$ is an irrational number.
∴ 2 – $\sqrt { 5 }$ is an irrational number.
(∵ The difference of a rational number and an irrational number is irrational)

(2) 3 + $\sqrt { 23 }$ – $\sqrt { 23 }$ = 3 (rational)

(3) $\cfrac { 2\sqrt { 7 } }{ 7\sqrt { 7 } }$ = $\cfrac { 2 }{ 7 }$ (rational)

(4) $\cfrac { 1 }{ \sqrt { 2 } }$ (irrational)  ∵ 1 ≠ 0 is a rational number and $\sqrt { 2 }$2 ≠ 0 is an irrational a/2 number.
∴ $\cfrac { 1 }{ \sqrt { 2 } }$ = is an irrational number.
(∵ The quotient of a non-zero rational number with an irrational number is irrational).
(5) 2π (irrational) ∵ 2 is a rational number and π is an irrational number.
∴  2π is an irrational number, (∵ The product of a non-zero rational number with an irrational number is an irrational).

Ex 1.5 Class 9 Maths Question 2.
Simplify each of the following expressions :
(1) (3 + $\sqrt { 3 }$ ) (2 + a/2)
(2) (3 + $\sqrt { 3 }$ ) (3- $\sqrt { 3 }$ )
(3) ( $\sqrt { 5 }$ + $\sqrt { 2 }$ )2
(4) ( $\sqrt { 5 }$ – $\sqrt { 2 }$ ) ( $\sqrt { 5 }$ + $\sqrt { 2 }$ )
Solution: Ex 1.5 Class 9 Maths Question 3.
Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is
π = $\cfrac { c }{ d }$. This seems to contradict the fact that it is irrational. How will you resolve this contradiction?
Solution:
Actually $\cfrac { c }{ d }$ = $\cfrac { 22 }{ 7 }$ which is an approximate value of π.

Ex 1.5 Class 9 Maths Question 4.
Represent $\sqrt { 9.3 }$ on the number line.
Solution:
Mark the distance 9.3 units from a fixed point A on a given line to obtain a point B such that AB = 9.3 units. From B, mark a distance of 1 unit and mark the new point as C. Find the mid-point of AC and mark that point as O. Draw a semi-circle with center O and radius OC. Draw a line perpendicular to AC passing through B and intersecting the semi-circle at D Then BD = $\sqrt { 9.3 }$. To represent $\sqrt { 9.3 }$ on the number line. Let us treat the line BC as the number line, with B as zero, C as 1, and so on. Draw an arc with center B and radius BD, which intersects the number line at point E. Then, the point E represent $\sqrt { 9.3 }$.

Ex 1.5 Class 9 Maths Question 5.
Rationalise the denominators of the following:
(i) $\cfrac { 1 }{ \sqrt { 7 } }$
(ii) $\cfrac { 1 }{ \sqrt { 7 } -\sqrt { 6 } }$
(iii) $\cfrac { 1 }{ \sqrt { 5 } +\sqrt { 2 } }$
(iv) $\cfrac { 1 }{ \sqrt { 7 } - { 2 } }$
Solution: We hope the NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5 help you. If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5, drop a comment below and we will get back to you at the earliest.

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