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

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 9 |

Subject |
Maths |

Chapter |
Chapter 1 |

Chapter Name |
Number Systems |

Exercise |
Ex 1.5 |

Number of Questions Solved |
5 |

Category |
NCERT Solutions |

## 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:**

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