Solve Nested Square Roots: √√49 × √√16 Multiplication Problem

Because $\sqrt{\sqrt{49}} \cdot \sqrt{\sqrt{16}}$ is not the same as $\sqrt{\sqrt{49 \times 16}}$! You must evaluate each nested radical separately first.

Work from the innermost radical outward. For $\sqrt{\sqrt{16}}$: first find $\sqrt{16} = 4$, then $\sqrt{4} = 2$. Stop when you can't simplify further.

Like with $\sqrt{\sqrt{49}}$! Since $\sqrt{49} = 7$ and 7 isn't a perfect square, you get $\sqrt{7}$ and leave it in radical form.

Yes, but be careful! For $\sqrt{\sqrt{49}}$, calculate $\sqrt{49} = 7$ first, then $\sqrt{7} \approx 2.646$. But keep exact answers like $2\sqrt{7}$ when possible.

Because $\sqrt{7}$ is irrational (never-ending, non-repeating decimal). The exact answer $2\sqrt{7}$ is more precise than any decimal approximation!