When is a radical in its simplest form? Seemingly conflicting answers

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Simply put, is a radical in its simplest form if all square factors are removed and radicand is still a (non-square) fraction? Like: $$\frac{1}{42}\sqrt\frac{1}{2}$$

This is the solution given on Khan Academy asking to simplify the below problem: $$-\sqrt\frac{1}{98} + \sqrt\frac{1}{72}$$

However, according to this site, "A radical is in its simplest form when the radicand is not a fraction."

So who's correct?

I tried to remove the fraction anyway. Is my solution correct?

$$\frac{1}{42}\sqrt\frac{1}{2} = \frac{1}{42}\sqrt\frac{1 \times 2}{2 \times 2}$$

$$\frac{1}{42}\sqrt\frac{1 \times 2}{2 \times 2} = \frac{1}{42}\sqrt\frac{2}{4} = \frac{1}{42} \times \frac{1}{2}\sqrt2$$

$$=\frac{1}{84}\sqrt2$$