(a) Evaluate and express your answer in standard form : \(\frac{4.56 \times 3.6}{0.12}\)
(b) Without using mathematical tables or calculator, evaluate \((73.8)^{2} – (26.2)^{2}\).
(c) Simplify \(\sqrt{1\frac{19}{81}}\), expressing your answer in the form \(\frac{a}{b}\) where a and b are positive integers.
Explanation
(a) \(\frac{4.56 \times 3.6}{0.12} \equiv \frac{4.56 \times 360}{12}\)
= \(4.56 \times 30 \)
= \(136.8 \)
= \(1.368 \times 10^{2}\)
(b) \((73.8)^{2} - (26.2)^{2}\)
Using the method of difference of two squares,
= \((73.8 + 26.2) \times (73.8 - 26.2)\)
= \(100 \times 47.6\)
= \(4760\)
(c) \(\sqrt{1\frac{19}{81}}\)
= \(\sqrt{\frac{100}{81}}\)
= \(\frac{10}{9}\)