**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 the part of NCERT Solutions for Class 9 Maths. Here you can find the NCERT Solutions for Class 9 Maths Chapter 1 Number System Ex 1.5.

**NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.1****NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2****NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.3****NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.4****NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5****NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.6**

**Ex 1.5 Class 9 Maths Question 1.****
**Classify the following numbers as
rational or irrational.

**Solution:**

(i)The difference between a rational number and an irrational number is always an irrational number.

(i)

∴ 2 – √5 is an irrational number.

**(ii)**(3 + √23) – √23 = 3 + √23 – √23 = 3

Here, 3 is a rational number. Thus, (3 + √23) – √23 is a rational number.

**(iii)**Since, 2√7/7√7 = 2/7, which is a rational number. Therefore, 2√7/7√7 is a rational number.

**(iv)**∵ The numerator is a rational number and the denominator is an irrational number. The quotient of a rational divided by an irrational number is an irrational number.

∴ 1/√2 is an irrational number.

**(v)**∵ 2Ï€ = 2 × Ï€ = Product of a rational number and an irrational number is an irrational number.

∴ 2Ï€ is an irrational number.

**Ex 1.5 Class 9 Maths Question 2.****
**Simplify each of the following
expressions.

**Solution:**

(i)(3 + √3)(2 + √2)

(i)

= 3(2 + √2) + √3(2 + √2)

= 6 + 3√2 + 2√3 + √6

Thus, (3 + √3)(2 + √2) = 6 + 3√2 + 2√3 + √6

**(ii)**(3 + √3)(3 – √3) = (3)

^{2}– (√3)

^{2}

= 9 – 3 = 6

Thus, (3 + √3)(3 – √3) = 6

**(iii)**(√5 + √2)

^{2}= (√5)

^{2}+ (√2)

^{2}+ 2(√5)(√2)

= 5 + 2 + 2√10 = 7 + 2√10

Thus, (√5 + √2)

^{2}= 7 + 2√10

**(iv)**(√5 – √2)(√5 + √2) = (√5)

^{2}– (√2)

^{2}

= 5 – 2
= 3

Thus, (√5 – √2) (√5 + √2) = 3

**Ex 1.5 Class 9 Maths Question 3.****
**Recall, Ï€ is defined as the ratio
of the circumference (say c) of a circle to its diameter (say d). That is Ï€
= c/d. This seems to contradict
the fact that Ï€ is irrational. How will you resolve this contradiction?

**Solution:****
**When we measure the length of a
line with a scale or with any other device, we only get an approximate rational
value, i.e., c and d both are approximate rational value.

∴ c/d is irrational and hence Ï€ is irrational.

Thus, there is no contradiction in saying that Ï€ is irrational.

**Ex 1.5 Class 9 Maths Question 4.****
**Represent √9.3 on the
number line.

**Solution:****
**Draw a line segment AB = 9.3 units
and extend it to C such that BC = 1 unit.

Find the mid-point of AC by bisecting the line segment AC and mark it as O.

Draw a semicircle taking O as centre and AO or OC as radius. Draw BD ⊥ AC.

Draw an arc taking B as centre and BD as radius meeting AC produced at E.

Now,
BE = BD = √9.3 units

**Ex 1.5 Class 9 Maths Question 5.**

Rationalise the denominators of the
following:

**Solution:**