Explanation

(a)110\(_x\) - 40\(_{5}\)

1 x  \(x^2}\) + 1 x \(x^1\) + 0 x \(x^o\)

x = 4 x 5\(^1\) + 0 x 5\(^o\)

x\(^2\) + x = 4 x 5 + 0

x\(^2\) + x - 20 = 0

(x - 4)(x + 5) = 0

x - 4 = 0 or x + 5 = 0

x = 4 or x = -5

x = 4

(b) Simplify \(\frac{15}{\sqrt{75}}\)  + \(\sqrt{108}\) + \(\sqrt{432}\)

 = \(\frac{15}{\sqrt{25 \times 3}}\)  + \(\sqrt{36 \times 3}\)

= \(\frac{15}{5 \sqrt{3}\) + 6\(\sqrt{3}\) + 12\(\sqrt{3}\)

= \(\frac{15 \sqrt{3}}{15 \times \sqrt{3} \times \sqrt{3}}\) + 18\(\sqrt{3}\)

= \(\frac{15\sqrt{3}}{15}\) + 18\(\sqrt{3}\)

\(\sqrt{3}\) + 18\(\sqrt{3}\) = 19\(\sqrt{3}\)

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