Question

plz prove 1/3-✓7 is an irrational number

Answer 1

HEYA MATE, HERE IS UR ANSWER


$<b><i>Let us assume that [tex]\frac{1}{3}$-$\sqrt{7}$ is a rational number .[/tex]

So , $\frac{1}{3}$-$\sqrt{7}$=$\frac {a}{b}$

$\frac {1}{3}$-$\frac {a}{b}$=$\sqrt {7}$

Since $\sqrt {7}$ is irrational. So ,our supposition is wrong .

Therefore, $\frac {1}{3}$-$\sqrt {7}$ is irrational.

$\huge\boxed{\mathbb{BE\:BRAINLY}}$

Answer 2

Let 1/3-√7 be rational no.

∴ 1/3-√7 = p/q

1/3-√7*3+√7/3+√7 = p/q

3+√7/(3)²-(√7)² = p/q

3+√7/9-7 = p/q

3+√7/2 = p/q

3+√7 = p/2q

Squaring both sides,

9+7+6√7 = (p/2q)²

6√7 = (p-2q)²-16

It is not possible because square of something cannot be equal to root of something. So, there is a contradiction.

Hence, 1/3-√7 is an irrational number.