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

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Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 9 |

Subject | Maths |

Chapter | Chapter 1 |

Exercise | Class 9 Chapter 16 Playing with Numbers Exercise 1.5 |

Number of Questions Solved | 6 |

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

**NCERT TEXTBOOK EXERCISES**

**Question 1.****Classify the following numbers as rational or irrational.**

**Solution:****(i)** Irrational âˆµ 2 is a rational number and âˆš5 is an irrational number.

âˆ´ 2.âˆš5 is an irrational number.

(âˆµThe difference of a rational number and an irrational number is irrational)**(ii)** 3 + âˆš23 â€“ âˆš23 = 3 (rational)**(iii)** $\frac { 2\sqrt { 7 } }{ 7\sqrt { 7 } }$ (rational)**(iv)** 1/âˆš2(irrational) âˆµ 1 â‰ 0 is a rational number andâˆš2â‰ 0 is an irrational number.

âˆ´ 1/âˆš2 is an irrational number. 42

(âˆµ The quotient of a non-zero rational number with an irrational number is irrational).**(v)** 2Ï€ (irrational) âˆµ 2 is a rational number and Ï€ is an irrational number.

âˆ´ 2x is an irrational number. ( âˆµThe product of a non-zero rational number with an irrational number is an irrational)

**Question 2.****Simplify each of the following expressions**

**Solution:**

**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 n is irrational. How will you resolve this contradiction?****Solution:**

Actually c/d = 22/7,which is an approximate value of Ï€.

**Question 4.****Represent âˆš9.3 on the number line.****Solution:**

Firstly we draw AB = 9.3 units. Now, from S, mark a distance of 1 unit. Let this point be C. Let O be the mid-point of AC. Now, draw aemi â€“ circle with centre O and radius OA. Let us draw a line perpendicular to AC passing through point B and intersecting the semi-circle at point D.

âˆ´ The distance BD = âˆš9.3

Draw an arc with centre B and radius BD, which intersects the number line at point E, then the point E represents âˆš9.3.

**Question 5.****Rationalise the denominator of the following**

**Solution:**

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

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