Question

√(81+18√(7)+7)
(not decimal form)

Answer 1

`\huge\boxed{√(81+18\sqrt7+7)=9+\sqrt7}`

Explanation:

`√(81+18\sqrt7+7)=(*)\\\\81=9^2\\7=(\sqrt7)^2\\18\sqrt7=(2)(9)(\sqrt7)\\\\(*)=√(9^2+(2)(9)(\sqrt7)+(\sqrt7)^2)\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\=√((9+\sqrt7)^2)\\\\\text{use}\ √(a^2)=|a|\\\\=|9+\sqrt7|=9+\sqrt7`