Question

Answer quickly please

Answer 1

1)
Let us assume that
$\sqrt{5}+ \sqrt{2} \: is \: rational$
Therefore, it can be expressed in p/q form, where p<q and p, a are not equal to zero.

$\sqrt{5} + \sqrt{2} = p \div p$
$\sqrt{5} = p \div q - \sqrt{2}$
(square on both sides)

$( \sqrt{5})^{2} = (p \div q - \sqrt{2} )^{2}$
$5 = ({p}^{2} \div {q}^{2} ) + 2 - (2p \sqrt{2} \div q)$
$5 = ({p }^{2} + 2 {q}^{2} - 2pq \sqrt{2}) \div {q}^{2}$

Here, q^2 | 5
Hence, q | 5.
Therefore, 5 can be expressed as a multiple q

i. e. 5=qc


The continuation of this sum is in the picture above.

Hope it helps!!!