Question

is root over 100 + root over 36 the same as root over (100+36).

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that}, \\ \sqrt{100}=\sqrt{2\times 2\times 5\times 5}=2\times 5=10 \\ \sqrt{36}=\sqrt{2\times 2\times 3\times 3}=2\times 3=6 \\ \mathrm{now},\sqrt{100}+\sqrt{36}=10+6=16 \\ \mathrm{but},\sqrt{100+36}=\sqrt{136}=\sqrt{2\times 2\times 2\times 17}=2\sqrt{2\times 17}=2\sqrt{34} \\ \mathrm{since},16\ne 2\sqrt{34} \\ \mathrm{so},\sqrt{100}+\sqrt{36}\ne \sqrt{100+36} \end{gathered}$$