Discussion

Explanation:

When we multiply numbers in non-decimal system, multiply them as we do in decimal system but write them according to the given base system.

Step 1: Multiplying unit’s digits.

Multiply them as decimal system i.e., 2 × 2 = 4.

Now write 4 in base 3 i.e., (4)₁₀ = (11)₃

Write 1 and carry over 1 as we do with normal multiplication.

​​​​​​​Step 2: Multiplying unit’s and ten’s digits.

Multiply them as decimal system i.e., 2 × 2 + 1 = 5.

Now write 5 in base 3 i.e., (5)₁₀ = (12)₃

Step 3: Multiplying ten’s and unit’s digits.

Multiply them as decimal system i.e., 2 × 2 = 4.

Now write 4 in base 3 i.e., (4)₁₀ = (11)₃

Step 4: Multiplying ten’s digits.

Multiply them as decimal system i.e., 2 × 2 + 1= 5.

Now write 5 in base 3 i.e., (5)₁₀ = (12)₃

Step 5: Add the two results obtained.

∴ (22)₃ × (22)₃ = (2101)₃.

Hence, 2101.

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