Solve Nested Square Roots: √√(100/25) × √√25 Multiplication Problem

Square roots don't simply 'cancel out' - they follow specific rules! Nested radicals like $\sqrt{\sqrt{x}}$ mean you take the square root twice, which gives you the fourth root: $x^{1/4}$.

You can multiply square roots using $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$ only after you've simplified each radical completely. Don't try to combine them while they're still nested!

Divide: $\frac{100}{25} = \frac{100 ÷ 25}{25 ÷ 25} = \frac{4}{1} = 4$. You can also think: 25 times what equals 100? The answer is 4!

$\sqrt{10}$ is the square root (second root), while $\sqrt[4]{10}$ is the fourth root. Our nested square roots $\sqrt{\sqrt{x}}$ would equal the fourth root, but we simplified first!

If the answer were 10, then $\sqrt{\sqrt{4}} \cdot \sqrt{\sqrt{25}}$ would need to equal 10. But $\sqrt{2} \cdot \sqrt{5} = \sqrt{10} ≈ 3.16$, not 10. Always work through each step carefully!