Question

What are the properties of $R$ used in the following? $\sqrt{2}(1+\sqrt{2})=2+\sqrt{2}$

Answer 1

We know that the distributive property of multiplication over addition for any three numbers $a,b$ and $c$ states that $a(b+c)=ab+ac$

Now, since it is given that $\sqrt{2}(1+\sqrt{2})=2+\sqrt{2}$ that is

$\sqrt{2}(1+\sqrt{2})=(\sqrt{2}\times 1)+(\sqrt{2}\times \sqrt{2})=\sqrt{2}+2=2+\sqrt{2}$

Hence, the distributive property of multiplication over addition is used in $\sqrt{2}(1+\sqrt{2})=2+\sqrt{2}$.