Question

show that (√2+√3) whole square is irrational ​

Answer 1

Answer:

(√2 + √3)²

= (√2)² + (√3)² + 2(√2)(√3)

= 2 + 3 + 2√6

= 5 + 2√6

you can see that

5 + 2√6

is irrational .

.......

Hope, it may Help you.✌️

Answer 2

Answer:

5 +2

$5 + 2 \sqrt{6}$

Step-by-step explanation:

we know that

$(a+b) {}^{2} = a {}^{2} + b {}^{2} + 2ab$

$substitute \: a = \sqrt{2 \: \: } \\ b = \sqrt{3}$

$( \sqrt{2} + \sqrt{3} ) {}^{2} = \\ ( \sqrt{2 {}^{} } ) {}^{2} +(\sqrt{3} ){}^{2}+ 2 \times \sqrt{2} \times \sqrt{3}$

$= 2 + 3 + 2 \sqrt{6}$

$= 5 + 2 \sqrt{6}$

here

$5 + \sqrt{6 \:} \: is \: a \: irrational \: number \: so \: whole \: expression \: is \: irrational$