Question

Prove that √3+√7 is irrational.​

Answer 1

Answer:

because root under 3 and root under 7 is irrational number show root under 3 + root 7 is irrational number

Answer 2

Answer:

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Step-by-step explanation:

LET us assume that

$\sqrt{3} + \sqrt{7}$

is a rational number

then,

squaring both sides

$( { \sqrt{3} + \sqrt{7} }^{2} = {r}^{2}$

$3 + 7 + \sqrt[2]{21} = {r}^{2}$

$\sqrt{21} = \frac{ {r}^{2} - 10 }{2}$

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Now, r²-10/2 is a rational no.as 'r' is a

rational number by Assumption

There is a contradiction with L.H.S

which is root 21 .

Thus

$\sqrt{21}$

is not a rational number

it means

$\sqrt{21}$

is irrational number