Question 12 Marks
Simplify: If $\sqrt[3]{729}=9$ then $\sqrt[3]{0.000729}=$ ?
View full question & answer→Questions
2 Mark Question
Take a timed test
30 questions · self-marked practice — reveal the answer and mark yourself.
Question 22 Marks
Simplify: $\sqrt[3]{\frac{16}{54}}$
Answer
View full question & answer→Solution is as follows.
Question 32 Marks
Simplify: $\sqrt[3]{\frac{27}{125}}$
View full question & answer→Question 42 Marks
Find the cube root of the following numbers.
32768
Answer
View full question & answer→32768
= 2 × 2 × 2 × 4 × 4 × 4 × 4 × 4 × 4
= (2 × 4 × 4) × (2 × 4 × 4) × (2 × 4 × 4)
= (2 × 4 × 4)³
= 32³
$\therefore \sqrt[3]{32768}=3$
\begin{tabular}{l|l}
\hline 2 & 32768 \\
\hline 2 & 16384 \\
\hline 2 & 8192 \\
\hline 4 & 4096 \\
\hline 4 & 1024 \\
\hline 4 & 256 \\
\hline 4 & 64 \\
\hline 4 & 16 \\
\hline 4 & 4 \\
\hline & 1 \\
\hline
\end{tabular}
= 2 × 2 × 2 × 4 × 4 × 4 × 4 × 4 × 4
= (2 × 4 × 4) × (2 × 4 × 4) × (2 × 4 × 4)
= (2 × 4 × 4)³
= 32³
$\therefore \sqrt[3]{32768}=3$
\begin{tabular}{l|l}
\hline 2 & 32768 \\
\hline 2 & 16384 \\
\hline 2 & 8192 \\
\hline 4 & 4096 \\
\hline 4 & 1024 \\
\hline 4 & 256 \\
\hline 4 & 64 \\
\hline 4 & 16 \\
\hline 4 & 4 \\
\hline & 1 \\
\hline
\end{tabular}
Question 52 Marks
Find the cube root of the following numbers.
-2744
Answer
View full question & answer→-2744
= 2 × 2 × 2 × 7 × 7 × 7
= (2 × 7) × (2 × 7) × (2 × 7)
= (2 × 7)³
= 14³
∴ -2744 = (-14) × (-14) × (-14)
= (-14)³
$\begin{aligned} & \therefore \sqrt[3]{-2744}=-14 \\ & \begin{array}{c|c}\hline 2 & 2744 \\ \hline 2 & 1372 \\ \hline 2 & 686 \\ \hline 7 & 343 \\ \hline 7 & 49 \\ \hline 7 & 7 \\ \hline & 1\end{array} \\ & \end{aligned}$
= 2 × 2 × 2 × 7 × 7 × 7
= (2 × 7) × (2 × 7) × (2 × 7)
= (2 × 7)³
= 14³
∴ -2744 = (-14) × (-14) × (-14)
= (-14)³
$\begin{aligned} & \therefore \sqrt[3]{-2744}=-14 \\ & \begin{array}{c|c}\hline 2 & 2744 \\ \hline 2 & 1372 \\ \hline 2 & 686 \\ \hline 7 & 343 \\ \hline 7 & 49 \\ \hline 7 & 7 \\ \hline & 1\end{array} \\ & \end{aligned}$
Question 62 Marks
Find the cube root of the following numbers.
-512
Answer
View full question & answer→-512
= 2 × 2 × 2 × 4 × 4 × 4
= (2 × 4) × (2 × 4) × (2 × 4)
= (2 × 4)³
= 8³
∴ – 512 = (- 8) × (- 8) × (- 8)
= (-8)³
$\therefore \sqrt[3]{-512}= -8$
\begin{tabular}{l:l}
\hline 2 & 512 \\
\hline 2 & 256 \\
\hline 2 & 128 \\
\hline 4 & 64 \\
\hline 4 & 16 \\
\hline 4 & 4 \\
\hline & 1
\end{tabular}
= 2 × 2 × 2 × 4 × 4 × 4
= (2 × 4) × (2 × 4) × (2 × 4)
= (2 × 4)³
= 8³
∴ – 512 = (- 8) × (- 8) × (- 8)
= (-8)³
$\therefore \sqrt[3]{-512}= -8$
\begin{tabular}{l:l}
\hline 2 & 512 \\
\hline 2 & 256 \\
\hline 2 & 128 \\
\hline 4 & 64 \\
\hline 4 & 16 \\
\hline 4 & 4 \\
\hline & 1
\end{tabular}
Question 72 Marks
Find the cube root of the following numbers.
343
Answer
View full question & answer→343
= 7 × 7 × 7
= 7³
\begin{tabular}{c:c}
$\therefore \sqrt[3]{343}=7$ \\
\hline 7 & 343 \\
\hline 7 & 49 \\
\hline 7 & 7 \\
\hline & 1
\end{tabular}
= 7 × 7 × 7
= 7³
\begin{tabular}{c:c}
$\therefore \sqrt[3]{343}=7$ \\
\hline 7 & 343 \\
\hline 7 & 49 \\
\hline 7 & 7 \\
\hline & 1
\end{tabular}
Question 82 Marks
Find the cube root of the following numbers.
729
Answer
View full question & answer→729
= (3 × 3) × (3 × 3) × (3 × 3)
= (3 × 3)³
= 9³
$
\begin{aligned}
&\therefore \sqrt[3]{729}=9\\
&\begin{array}{l|l}
3 & 729 \\
\hline 3 & 243 \\
\hline 3 & 81 \\
\hline 3 & 27 \\
\hline 3 & 9 \\
\hline 3 & 3 \\
\hline & 1
\end{array}
\end{aligned}
$
= (3 × 3) × (3 × 3) × (3 × 3)
= (3 × 3)³
= 9³
$
\begin{aligned}
&\therefore \sqrt[3]{729}=9\\
&\begin{array}{l|l}
3 & 729 \\
\hline 3 & 243 \\
\hline 3 & 81 \\
\hline 3 & 27 \\
\hline 3 & 9 \\
\hline 3 & 3 \\
\hline & 1
\end{array}
\end{aligned}
$
Question 92 Marks
Find the cube root of the following numbers.
8000
Answer
View full question & answer→8000
= 2 × 2 × 2 × 10 × 10 × 10
= (2 × 10) × (2 × 10) × (2 × 10)
= (2 × 10)³
= 20³
\begin{tabular}{c|l}
$\therefore \sqrt[3]{8000}=20$ \\
\hline 2 & 8000 \\
\hline 2 & 4000 \\
\hline 2 & 2000 \\
\hline 10 & 1000 \\
\hline 10 & 100 \\
\hline 10 & 10 \\
\hline & 1 \\
\hline
\end{tabular}
= 2 × 2 × 2 × 10 × 10 × 10
= (2 × 10) × (2 × 10) × (2 × 10)
= (2 × 10)³
= 20³
\begin{tabular}{c|l}
$\therefore \sqrt[3]{8000}=20$ \\
\hline 2 & 8000 \\
\hline 2 & 4000 \\
\hline 2 & 2000 \\
\hline 10 & 1000 \\
\hline 10 & 100 \\
\hline 10 & 10 \\
\hline & 1 \\
\hline
\end{tabular}
Question 102 Marks
Write in the form ‘nth root of a’ in each of the following numbers.
$(6)^{\frac{1}{7}}$
Answer
View full question & answer→Seventh root of 6.
Question 112 Marks
Write in the form ‘nth root of a’ in each of the following numbers.
$(100)^{\frac{1}{19}}$
Answer
View full question & answer→Nineteenth root of 100.
Question 122 Marks
Write in the form ‘nth root of a’ in each of the following numbers.
$(512)^{\frac{1}{9}}$
Answer
View full question & answer→Ninth root of 512.
Question 132 Marks
Write in the form ‘nth root of a’ in each of the following numbers.
$(15)^{\frac{1}{5}}$
Answer
View full question & answer→Fifth root of 15.
Question 142 Marks
Write in the form ‘nth root of a’ in each of the following numbers.
$(49)^{\frac{1}{2}}$
Answer
View full question & answer→Square root of 49.
Question 152 Marks
Write in the form ‘nth root of a’ in each of the following numbers.
$(81)^{\frac{1}{4}}$
Answer
View full question & answer→Fourth root of 81.
Question 162 Marks
Express the following numbers in index form. : Seventh root of 30
Answer
View full question & answer→$(30)^{\frac{1}{7}}$
Question 172 Marks
Express the following numbers in index form. : Eighth root of 100
Answer
View full question & answer→$(100)^{\frac{1}{8}}$
Question 182 Marks
Express the following numbers in index form. : Cube root of 17
Answer
View full question & answer→$(17)^{\frac{1}{3}}$
Question 192 Marks
Express the following numbers in index form. : Square root of 256
Answer
View full question & answer→$(256)^{\frac{1}{2}}$
Question 202 Marks
Express the following numbers in index form. : Sixth root of 9
Answer
View full question & answer→$(9)^{\frac{1}{6}}$
Question 212 Marks
Express the following numbers in index form. : Fifth root of 13
Answer
View full question & answer→$(13)^{\frac{1}{5}}$
Question 222 Marks
Using laws of indices, write proper numbers in the following boxes.
$\left(\frac{5}{7}\right)^{-3}=\left(\frac{()}{()}\right)^3$
Answer
View full question & answer→$\left(\frac{5}{7}\right)^{-3}=\left(\frac{7}{5}\right)^3$
Question 232 Marks
Using laws of indices, write proper numbers in the following boxes.
$\left(\frac{5}{7}\right)^3=\frac{()^3}{()^3}$
Answer
View full question & answer→$\left(\frac{5}{7}\right)^3=\frac{5^3}{7^3}$
Question 242 Marks
Using laws of indices, write proper numbers in the following boxes.
$(5 \times 7)^2=5^{()} \times 7^{()}$
Answer
View full question & answer→$(5 \times 7)^2=5^2 \times 7^2$
Question 252 Marks
Using laws of indices, write proper numbers in the following boxes.
$5^1=()$
Answer
View full question & answer→$5^1=5$
Question 262 Marks
Using laws of indices, write proper numbers in the following boxes.
$5^0=()$
Answer
View full question & answer→$5^0=1$
Question 272 Marks
Using laws of indices, write proper numbers in the following boxes.
$5^{-3}=\frac{1}{5^0}$
Answer
View full question & answer→$5^{-3}=\frac{1}{5^3}$
Question 282 Marks
Using laws of indices, write proper numbers in the following boxes.
$\left(3^4\right)^5=3^{()}$
Answer
View full question & answer→$\left(3^4\right)^5=3^{20}$
Question 292 Marks
Using laws of indices, write proper numbers in the following boxes.
$3^7 \div 3^9=3^{()}$
Answer
View full question & answer→$3^7 \div 3^9=3^{-2}$
Question 302 Marks
Using laws of indices, write proper numbers in the following boxes.
$3^5 \times 3^2=3^{()}$
Answer
View full question & answer→$3^5 \times 3^2=3^7$