Prove that the following number is irrational: 2 3 - 7

Let 2 3 - 7 is rational number equal to r . ⇒ 2 3 - 7 = r ⇒ r + 7 2 = 3 If 2 , 7 , r are rational numbers, then 3 is also rational number. This contradicts the fact that 3 is irrational. Thus, we get 2 3 - 7 is irrational. Hence, it is proved that 2 3 - 7 are irrational.

Prove that the following number is irrational: 2 3 - 7

Let 2 3 - 7 is rational number equal to r . ⇒ 2 3 - 7 = r ⇒ r + 7 2 = 3 If 2 , 7 , r are rational numbers, then 3 is also rational number. This contradicts the fact that 3 is irrational. Thus, we get 2 3 - 7 is irrational. Hence, it is proved that 2 3 - 7 are irrational.

Locate 10 and 17 on the number line.

We write 10 and 17 as the sum of squares of two natural numbers. Thus, we get: 10 = 3 2 + 1 and 17 = 4 2 + 1 Let l be the number line and point O represents the number 0 on the number line. Mark a point A such that, A represents the number 3 , then the length of line segment = 3 u n i t s . At A draw A C ⊥ O A . From A C cut off A B = 1 u n i t . By Pythagoras theorem, in ∆ O A B , O B 2 = O A 2 + A B 2 . O B = 3 2 + 1 = 10 u n i t s With O as centre and radius as O B , we draw an arc of a circle to meet the number line l at point P . As O P = O B = 10 u n i t s , the point P represents the number 10 on the number line. Similarly, Mark a point D such that, D represents the number 4 , then the length of line segment = 4 u n i t s . At D draw D E ⊥ O D . From D E cut off D F = 1 u n i t . By Pythagoras theorem, in ∆ O D F , O F 2 = O D 2 + D F 2 . O F = 4 2 + 1 = 17 u n i t s With O as centre and radius as O F , we draw an arc of a circle to meet the number line l at point Q . As O Q = O F = 17 u n i t s , the point Q represents the number 17 on the number line. Hence, below given is a number line on which 10 and 17 is marked.

E M B I B E

Understanding ICSE Mathematics Class 9>Chapter 1 - Rational and Irrational Numbers>EXERCISE 1.2>Q 8

EASY

9th ICSE

IMPORTANT

Earn 100

Prove that the following number is irrational:

$2 \sqrt{3} - 7$

Important Questions on Rational and Irrational Numbers

EASY

9th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 9>Chapter 1 - Rational and Irrational Numbers>EXERCISE 1.2>Q 8

Prove that the following number is irrational:

$\sqrt{2} + \sqrt{5}$

MEDIUM

9th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 9>Chapter 1 - Rational and Irrational Numbers>EXERCISE 1.3>Q 1

Locate $\sqrt{10}$ and $\sqrt{17}$ on the number line.

MEDIUM

9th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 9>Chapter 1 - Rational and Irrational Numbers>EXERCISE 1.3>Q 4

Without actually performing long division, find if $\frac{987}{10500}$ will have terminating or non-terminating repeating decimal expansion. Give reasons for your answer.

MEDIUM

9th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 9>Chapter 1 - Rational and Irrational Numbers>EXERCISE 1.3>Q 5

Write the decimal expansion of following number and see whether it has terminating decimal expansion or not.

$\frac{17}{8}$

MEDIUM

9th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 9>Chapter 1 - Rational and Irrational Numbers>EXERCISE 1.3>Q 5

Write the decimal expansion of following number and see whether it has terminating decimal expansion or not.

$\frac{13}{3125}$