State whether the statement: Every point on the number line is of the form m , where m is a natural number is true or false. Justify your answer.

On number line positive numbers are placed to the right of zero and negative numbers are placed to the left of zero. We know that, Square root of negative numbers cannot be determined. Therefore, The negative numbers on the number line cannot be expressed in the form m . Hence, The given statement is false.

Show how 5 can be represented on the number line.

To represent 5 on the number line, take O A = 2 units and make a perpendicular at A , so that A B = 1 unit , as shown in the figure. Then, ∆ O A B is a right-angled triangle So, by applying Pythagoras theorem, we get, O B 2 = O A 2 + A B 2 . ⇒ O B 2 = 2 2 + 1 2 ⇒ O B 2 = 5 ⇒ O B = 5 units . Now, taking O as Centre and O B as radius, draw an arc intersecting the number line at P . Hence, O P is the required distance that represents 5 .

E M B I B E

Mathematics 9 Part I>Chapter 1 - Number Systems>EXERCISE

Karnataka Board Solutions for Chapter: Number Systems, Exercise 2: EXERCISE

Author:Karnataka Board

Karnataka Board Mathematics Solutions for Exercise - Karnataka Board Solutions for Chapter: Number Systems, Exercise 2: EXERCISE

Attempt the free practice questions on Chapter 1: Number Systems, Exercise 2: EXERCISE with hints and solutions to strengthen your understanding. Mathematics 9 Part I solutions are prepared by Experienced Embibe Experts.

Questions from Karnataka Board Solutions for Chapter: Number Systems, Exercise 2: EXERCISE with Hints & Solutions

EASY

9th Karnataka Board

IMPORTANT

Mathematics 9 Part I>Chapter 1 - Number Systems>EXERCISE>Q 1

State whether the statement: Every irrational number is a real number is true or false. Justify your answer.

EASY

9th Karnataka Board

IMPORTANT

Mathematics 9 Part I>Chapter 1 - Number Systems>EXERCISE>Q 1

State whether the statement: Every point on the number line is of the form $\sqrt{m},$ where $m$ is a natural number is true or false. Justify your answer.

EASY

9th Karnataka Board

IMPORTANT

Mathematics 9 Part I>Chapter 1 - Number Systems>EXERCISE>Q 1

State whether the statement: Every real number is an irrational number is true or false. Justify your answer.

EASY

9th Karnataka Board

IMPORTANT

Mathematics 9 Part I>Chapter 1 - Number Systems>EXERCISE>Q 2

Are the square roots of all positive integers irrational? If not, give an example of the square root of a number, that is a rational number.

MEDIUM

9th Karnataka Board