NCERT Solutions for Class 9 Maths Exercise 1.5

myCBSEguide App

CBSE, NCERT, JEE Main, NEET-UG, NDA, Exam Papers, Question Bank, NCERT Solutions, Exemplars, Revision Notes, Free Videos, MCQ Tests & more.

NCERT solutions for Class 9 Maths Number Systems

NCERT Solutions for Class 9 Maths Number Systems

1. Classify the following numbers as rational or irrational:

(i)

(ii)

(iii)

(iv)

(v)

(i)

We know that

which is also an irrational number.

Therefore, we conclude thatis an irrational number.

(ii)

= 3

Therefore, we conclude thatis a rational number.

(iii)

We can cancelin the numerator and denominator, asis the common number in numerator as well as denominator, to get

Therefore, we conclude thatis a rational number.

(iv)

We know that.

We can conclude that, when 1 is divided by, we will get an irrational number.

Therefore, we conclude thatis an irrational number.

(v)

We know that

We can conclude thatwill also be an irrational number.

Therefore, we conclude thatis an irrational number.

NCERT Solutions for Class 9 Maths Exercise 1.5

2. Simplify each of the following expressions:

(i)

(ii)

(iii)

(iv)

Ans. (i)

We need to apply distributive law to find value of.

Therefore, on simplifying, we get.

(ii)

We need to apply distributive law to find value of.

Therefore, on simplifying, we get 6.

(iii)

We need to apply the formula to find value of.

=6

Therefore, on simplifying, we get.

(iv)

We need to apply the formula to find value of.

= 5-2

=3

Therefore, on simplifying, we get 3.

NCERT Solutions for Class 9 Maths Exercise 1.5

3. Recall, is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is,. This seems to contradict the fact that is irrational. How will you resolve this contradiction?

Ans. We know that when we measure the length of a line or a figure by using a scale or any device, we do not get an exact measurement. In fact, we get an approximate rational value. So, we are not able to realize that either circumference (c) or diameter(d) of a circle is irrational.

Therefore, we can conclude that as such there is not any contradiction regarding the value of and we realize that the value ofis irrational.

NCERT Solutions for Class 9 Maths Exercise 1.5

4. Represent 9.3 on the number line.

Ans. 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 call the new point as C. Find the mid-point of AC and call that point as O. Draw a semi-circle with centre O and radius OC = 5.15 units. Draw a line perpendicular to AC passing through B cutting the semi-circle at D. Then BD =

NCERT Solutions for Class 9 Maths Exercise 1.5

(i)

(ii)

(iii)

(iv)

Ans. (i)

We need to multiply the numerator and denominator ofby, to get

.

Therefore, we conclude that on rationalizing the denominator of, we get.

(ii)

We need to multiply the numerator and denominator ofby, to get

.

We need to apply the formulain the denominator to get

Therefore, we conclude that on rationalizing the denominator of, we get.

(iii)

We need to multiply the numerator and denominator ofby, to get

.

We need to apply the formulain the denominator to get

Therefore, we conclude that on rationalizing the denominator of, we get.

(iv)

We need to multiply the numerator and denominator ofby, to get

.

We need to apply the formulain the denominator to get

Therefore, we conclude that on rationalizing the denominator of, we get.

NCERT Solutions for Class 9 Maths Exercise 1.5

NCERT Solutions Class 9 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 9 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 9 Maths have total 15 chapters. 9 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 9 solutions PDF and Maths ncert class 9 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

CBSE app for Class 9

To download NCERT Solutions for Class 9 Maths, Computer Science, Home Science,Hindi ,English, Social Science do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through the best app for CBSE students and myCBSEguide website.

Test Generator

Create question papers online with solution using our databank of 5,00,000+ questions and download as PDF with your own name & logo in minutes.