Join Sarthaks eConnect Today - Largest Online Education Community!
0 votes
79 views
asked in Mathematics by (21.7k points)
edited by

In the following equations, find which variables x, y, z etc. represent rational or irrational numbers: 

(i)  x2 = 5

 (ii)  y2 = 9 

(iii)  z2 = 0.04

 (iv)  u2 = 17/ 4

(v)  v2 = 3

 (vi) w2 = 27 

vii)  t2 = 0.4

Sarthaks Test For Class 7-12

1 Answer

0 votes
answered by (21.7k points)
selected by
 
Best answer

(i) We have

 x2 = 5

Taking square root on both sides.

=> x2 = 5

=> x = 5

5 is not a perfect square root, so it is an irrational number. 

(ii) We have

   y2 = 9

  => y = 9

  =3

 =3/1

9 can be expressed in the form of p/q, so it a rational number.

(iii) We have

   z= 0.04

  Taking square root on both sides, we get,

z=0.04

=> z = 0.04

= 0.2

= 2/10

= 1/5

z can be expressed in the form of p/q, so it is a rational number.

(iv) We have

 u2 =17/4

Taking square root on both sides, we get,

u=17/4

=> u = 17/2

Quotient of an irrational and a rational number is irrational, so u is an irrational number.

(v) We have

  v= 3

 Taking square root on both sides, we get,

v13

=> v = 3

3 is not a perfect square root, so y is an irrational number.

(vi) We have

  w= 27

 Taking square root on both sides, we get,

 √w2  27

 => w = 3 x 3 x 3

 =33

 Product of a rational and an irrational is irrational number, so w is an irrational number. 

(vii) We have

  t= 0.4

 Taking square root on both sides, we get

 √t0.4

 => t = 4/10

 = 2/10

Since, quotient of a rational and an irrational number is irrational number, so t is an irrational number.

Related questions

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

One Thought Forever

“There is a close connection between getting up in the world and getting up in the morning.“
– Anon
~~~*****~~~

Categories

...