Match List I with List II Choose the correct answer from the options given…

Concept

To match a number with its square root, find the value whose square reproduces the number — test each candidate r against r² = N. A perfect square ending in 9 has a root ending in 3 or 7; one ending in 1 has a root ending in 1 or 9; one ending in 4 has a root ending in 2 or 8. The digit-count of N also bounds the root: a 5-digit perfect square has a 3-digit root, a 3-digit perfect square has a 2-digit root.

Application

Compute the exact square root of each List I number and read off the List II label that carries that value:

1. 81 → √81 = 9, since 9² = 81. The value 9 is List II label I.

2. 841 → √841 = 29, since 29² = 841. The value 29 is List II label II.

3. 53824 → √53824 = 232, since 232² = 53824. The value 232 is List II label III.

4. 41209 → √41209 = 203, since 203² = 41209. The value 203 is List II label IV.

Cross-check

Square each chosen root back to confirm: 203² = 41209, 29² = 841, 9² = 81, 232² = 53824 — every product reproduces its List I number, so the mapping is consistent.

Therefore A → IV, B → II, C → I, D → III.