Question

prove that root 3 + 2 root 7 is an irrational​

Answer 1

Step-by-step explanation:

ROOT 3+2 ROOT 7=2 ROOT TEN

SO IT IS IRRATIONAL

Answer 2

Answer:

$3 + 2 \sqrt{7} \: is \: a \: irrational \: number.$

Step-by-step explanation:

Let take that

$3 + 2 \sqrt{7} is \: a \: irrational \: number.$

So,We can write this answer as

$3 + 2 \sqrt{7} = \frac{x}{y}$

Here x and y use two coprime number and y not equal to zero.

$2 \sqrt{7} = \frac{x}{y} - 3 \\ \: 2 \sqrt{7} = \frac{x - 3y}{y} \\ \sqrt{7} = \frac{x - 3y}{2y}$

Here x and y are integer so,

$\frac{x - 3y}{2y} is \: a \: rational \: number \\ so \: \sqrt{7} should \: be \: a \: rational \: number \: but \: \sqrt{7} is \: a \: irrational \: number.$

so, It is contradict

Hence ,

$3 + 2 \sqrt{7} \: is \: a \: irrational \: number.$