Question

prove that 11+ 2√3 is irrational with full explanation
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Answer 1

$\Large \fbox \red {Question \: :}$

Prove that 11 + 2√3 is irrational.

$\Large \fbox \red {Answer \: :}$

We know that,

We cannot convert √3 in the form p/q.

So, 2√3 is irrational.

And, we also know that,

Rational + Irrational = Irrational

$\implies$ So, we can say that 11+ 2√3 is irrational.

$\therefore$ $\large \purple {Hence, \: PROVED!!}$

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$\Large \mathcal \pink {HOPE \:  IT \: HELPS}$ ❤️

$\huge \green {Brainliest \: please}$ ✌️

Answer 2

Answer:

its simple

Step-by-step explanation:

Let us assume to the contrary that √3 is a rational number.

It can be expressed in the form of p/q

where p and q are co-primes and q≠ 0.

⇒ √3 = p/q

⇒ 3 = p2/q2 (Squaring on both the sides)

⇒ 3q2 = p2………………………………..(1)

This means that 3 divides p2. This means that 3 divides p because each factor should appear two times for the square to exist.

So we have p = 3r

⇒ p2 = 9r2………………………………..(2)

from equation (1) and (2)

⇒ 3q2 = 9r2

⇒ q2 = 3r2

Where q2 is multiply of 3 and also q is multiple of 3.

so is $\sqrt[]{3}$  irrational no so

2$\sqrt[]{3}$ is also an irrational no because rational * irrational is irrational so

11 + 2$\sqrt[]{3}$ is also irrational ( rational + irrational = irrational)

hence proved

hope it helps