(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...
Question 1 Report
(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.
Answer Details
(a)
\[\frac{4.56\times3.6}{0.12} = \frac{16.416}{0.12} = 136.8 = 1.368\times10^{2}.\]
(b) Use the difference of two squares \(a^2 - b^2 = (a-b)(a+b)\):
\[(73.8)^2 - (26.2)^2 = (73.8 - 26.2)(73.8 + 26.2) = 47.6\times100 = 4760.\]
(c) Convert the mixed number to an improper fraction:
\[1\tfrac{19}{81} = \frac{81 + 19}{81} = \frac{100}{81},\qquad \sqrt{\frac{100}{81}} = \frac{10}{9}.\]
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