The fourth root of 2001200120012001 (that is, $\sqrt[4]{2001200120012001}$ ) is closest to
(A) 2001
(B) 6700
(C) 21000
(D) 12000
(E) 2100
The fourth root of 2001200120012001 (that is, $\sqrt[4]{2001200120012001}$ ) is closest to
(A) 2001
(B) 6700
(C) 21000
(D) 12000
(E) 2100

## Solution

2001200120012001 is roughly $2 \times 10^{15}=2000 \times 10^{12}$.

So the quantity desired is roughly $\sqrt[4]{2000 \times 10^{12}}=\sqrt[4]{2000} \times 10^{3} \approx 7 \times 10^{3}$ which is closest to 6700 .

ANSWER: (B)