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Evaluate $202^2_{three} - 112^2_{three}$
...

Evaluate $202^2_{three} - 112^2_{three}$

A.

21120

B.

21121

C.

21112

D.

21011

View answer & explanation

Correct answer is A

$202^2_{three}$ 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
$\begin{matrix} 3 & 204\\ 3 & 69 &R0\\ 3 & 22 & R2\\ 3 & 7 & R1\\ 2 & 2 & R1\\ & 0& R2 \uparrow\\ \end{matrix} \\ =21120_3$

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