Find the positive square root of the base 7 number \({(551662)_7}\), giving your answer as a base 7 number.

converting to base 10

\({(551662)_7} = 2 + 6 \times 7 + 6 \times {7^2} + 1 \times {7^3} + 5 \times {7^4} + 5 \times {7^5}\)     (M1)

\( = 96721\)     (A1)

\(\sqrt {96721}  = 311\)     A1

converting back to base 7

\(7)\underline {311} \)     (M1)

\()\underline {44} (3\)

\()\underline 6 (2\)     (A1)

it follows that \(\sqrt {{{(551662)}_7}}  = {(623)_7}\)     A1

Note: Accept \(623\).

[6 marks]