Calculating expressions to the power of two with radicals

Question

How do we calculate $(2\sqrt{22})^2$?

I tried but failed: $$ 2*2+2*\sqrt{22}+ \sqrt{22}*2+\sqrt{22}*\sqrt{22} $$ The answer is 88. Thanks!

Answer 1

When you see an expression like $ab$, it means $a\cdot b$, not $a+b$. Thus

$$2\sqrt{22}\equiv 2\cdot\sqrt{22},$$

and there's no need to distribute multiplication $a^2=aa$ over factors of $2$ and $\sqrt{22}$. Distribution is only needed over terms of a sum, not product.