Question

√(81+18√(7)+7) (not decimal form)

Answer 1

Answer:

$\huge\boxed{\sqrt{81+18\sqrt7+7}=9+\sqrt7}$

Step-by-step explanation:

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