Published on February 17th 2025 | 1 min , 186 words
Find the cube of the following numbers
\( 14^3 = 14 \times 14 \times 14 \)
\( = 2744\)
b) 9
\(9^3 = 9 \times 9 \times 9 \)
\( = 729\)
c) 2.3
\(2.3^3 = 2.3 \times 2.3 \times 2.3\)
\(=12.167\)
Use Mathematical tables to find the reciprocal of 0.0247, hence evaluate \(\frac{\sqrt[3]{3.025}}{0.0247}\) Correct to 2 d.p (3 marks)
\(\sqrt[3]{3.025} = 1.4462\)
\(\frac{1}{0.0247} \)
\(= (0.0247)^{-1}\)
\(= (2.47 \times 10^{-2})^{-1}\)
\(= 0.4049 \times 10^2\)
\(= 40.49\)
Use reciprocal, square and square root tables to evaluate, to 4 significant figures, the expression
\(
\sqrt{\frac{1}{24.56} + 4.346^2}
\)
\(
24.56 = 2.456 \times 10
\)
\(
4.346^2 = 18.89
\)
\(
\sqrt{\frac{1}{2.456 \times 10} + 18.89}
\)
\(
= \sqrt{\frac{1}{2.456} \times \frac{1}{10} + 18.89}
\)
\(
= \sqrt{\left( 0.4072 \times \frac{1}{10} \right) + 18.89}
\)
\(
= \sqrt{0.04072 + 18.89}
\)
\(
= \sqrt{18.93072}
\)
\(
= \sqrt{18.93}
\)
\(
= 4.351 \quad \text{(Answer)}
\)
Use squares, square roots and reciprocal tables to evaluate (3mks)
\(
3.045^2 + \frac{1}{\sqrt{49.24}}
\)
\(
3.045^2 = 9.272
\)
\(
\sqrt{49.24} = 7.017
\)
\(
\frac{1}{7.017} = 0.1425
\)
\(
9.272 + \frac{1}{7.017}
\)
\(
= 9.272 + 0.1425
\)
\(
= 9.4175
\)
Find the cubes of each of the following numbers:
(a) 15.3 (b) 2341 (c) 0.16 (d) 0.00472
Solutions
(a) \( (15.3)^3 \)
\( = 15.3 \times 15.3 \times 15.3 \)
\( = 1.53 \times 10 \times 1.53 \times 10 \times 1.53 \times 10 \)
\( = (1.53)^3 \times (10)^3 \)
\( = 3.582 \times 1\ 000 \)
\( = 3\ 582 \)
(b) \( (2\ 341)^3 \)
\( = (2.341 \times 10^3)^3 \)
\( = 2.341^3 \times 10^9 \)
\( = 12.829 \times 10^9 \)
\( = 1.2829 \times 10^1 \times 10^9 \)
\( = 1.2829 \times 10^{10} \)
\( \approx 1.283 \times 10^{10} \) (correct to 4 s.f.)
(c) \( (0.16)^3 \)
\( = (1.6 \times 10^{-1})^3 \)
\( = 1.6^3 \times 10^{-3} \)
\( = 4.096 \times 10^{-3} \)
\( = 0.004096 \)
(d) \( (0.00472)^3 \)
\( = (4.72 \times 10^{-3})^3 \)
\( = 4.72^3 \times 10^{-9} \)
\( = 105.15 \times 10^{-9} \)
\( = 1.0515 \times 10^2 \times 10^{-9} \)
\( = 1.0515 \times 10^{-7} \)
\( \approx 1.052 \times 10^{-7} \) (correct to 4 s.f.)