Correct Answer: Option A

Explanation

\(202^2_{three}\)when converted to base ten \(=(202_3)^2\)
202_3 = 2 \(\times 3^2 + 0 \times 3^1 + 2\times 3^0 = 18 + 0 + 2\)
=20\(_{ten}; (202_3)^2 = (20)^2_{ten} = 400\)
112\(^2_{three}\)when converted to base ten \(= (112_3)^2\)
112_3 = 1 \(\times 3^2 + 1 \times 3^1 + 2\times 3^0 = 9+3+2=14_{ten}\)
(112_3)\(^2 = (14)^2_{ten} = 196_{ten}\)
Evaluate \(\Longrightarrow 400-196 = 204\)
Reconvert to base three

204 ÷ 3 = 68 remainder 0

68 ÷ 3 = 22 remainder 2

22 ÷ 3 = 7 remainder 1

7 ÷ 3 = 2 remainder 1

2 ÷ 3 = 0 remainder 2

= 21120\(_3\)

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