(a) \(1001_{2} = 1 \times 2^{3} + 0 \times 2^{2} + 0 \times 2^{1} + 1 \times 2^{0}\)
= \(8 + 0 + 0 + 1\)
= 9
\(\sqrt{9} = 3_{10}\)

2	3
2	1 r 1
	0 r 1

\(\therefore \sqrt{1001_{2}} = 11_{2}\)
(b) In \(\Delta QOP, OQ = OP\)
\(\therefore QK = KP\)
\(\Delta QOK = \Delta POK\) (right- angled triangle)
In \(\Delta POK\),
\(OP^{2} = PK^{2} + OK^{2}\)
\(x^{2} = y^{2} + (\frac{z}{2})^{2}\)
\(\frac{z^{2}}{4} = x^{2} - y^{2}\)
\(z^{2} = 4x^{2} - 4y^{2}\)
\(z = \sqrt{4(x^{2} - y^{2})}\)
\(z = 2\sqrt{x^{2} - y^{2}}\)
(c)(i) \(< PSQ = \frac{1}{2}(< POQ) = \frac{1}{2}(160°)\)
= 80°
In \(\Delta PSQ\),
\(< PQS + < QPS + < PSQ = 180°\)
\(40° + < QPS + 80° = 180°\)
\(< QPS = 180° - 120° = 60°\)
(ii) \(< PSR = < PSQ + < QSR\)
= \(80° + 45°\)
= \(125°\)
\(< PQS = < PQO + < RQS \)
= \(40° + < RQS\)
\(< PSR + < PQS = 180°\)
\(\therefore 125° + 40° + < RQS = 180°\)
\(< RQS = 180° - 165°\)
= \(15°\)