Question

Can we write it like this? - root2+3=root2+root3​

Answer 1

Answer:

yes of course we can..............

Answer 2

Showing results for

Can we write it like this?

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

Answer :- No.

Proof

If

$\sqrt{2+3} = \sqrt{2}+\sqrt{3} \\ \dashrightarrow \sqrt{5} = \sqrt{2} + \sqrt{3} \\ \\ \rm Then,\ on \ squaring \ both \ the \ sides \ we \ get, \\ \dashrightarrow (\sqrt{5})^2 = \bigg ( \sqrt{2}+\sqrt{3} \bigg )^2 \\ \rm Since, \ (a+b)^2 = a^2+b^2+2ab , \therefore \\ \\ \dashrightarrow 5 = (\sqrt{2})^2 + (\sqrt{3})^2 + 2 \times \sqrt{2} \times \sqrt{3}$

$\dashrightarrow 5 = 2+ 3 + 2 \sqrt{6}$

$\dashrightarrow 5 = 5+ 2 \sqrt{6}$

∴ It's clearly false.

Hence,

$\sqrt{2+3} \neq \sqrt{2}+\sqrt{3}$

hope it helps