Question

prove that 7 root 3 divided by 11 is irrational

Answer 1

Step-by-step explanation:

Given:

$\frac{7 \sqrt{3} }{11}$

To find: Prove that the given number is irrational.

Solution: This type of proof can be easily done by theory of contradiction.

We know that √3 is irrational number.(It is given in such type of questions)

Let us assume that 7√3/11 is rational number,thus it can be expressed as a/b,b≠0

Thus,

$\frac{7 \sqrt{3} }{11} = \frac{a}{b} \\ \\ or \\ \\ \sqrt{3} = \frac{11a}{7b} \\ \\ or \\ \\ \sqrt{3} = \frac{c}{d} \\ \\ \: let \: 11a = c \: \: and \: \: 7b = d \: \: both \: are \: constant\:integer$

Here,

√3=c/d,

which cannot be possible for any irrational numbers.

Thus, by the theory of contradiction we can say that 7√3/11 is an irrational number.

Alternative solution:

We know that when rational number multiply with irrational number the result will always be irrational.

here

$\frac{7 \sqrt{3} }{11} = \frac{7}{11} \times \sqrt{3}$

7/11 is rational number

√3 is irrational

Thus, multiplication of both will give irrational number.

Thus,

7√3/11 is an irrational number.

Hope it helps you.

To learn more on brainly:

proof that √2 is irrational

https://brainly.in/question/2367037