Courses
Courses for Kids
Free study material
Offline Centres
More
Last updated date: 05th Dec 2023
Total views: 280.5k
Views today: 2.80k

# Making use of the cube root table, find the cube roots of the 833 (correct to three decimal places).

Verified
280.5k+ views
Hint: Consider the given number 833 between 830 and 840. Take cube root of all the three numbers and write it in the form ${{\left( 830 \right)}^{\dfrac{1}{3}}} < {{\left( 833 \right)}^{\dfrac{1}{3}}} < {{\left( 840 \right)}^{\dfrac{1}{3}}}$. Using the cube root table find the cube roots of 830 and 840. Observe the difference in the cube roots of 830 and 840 for the difference of 10 between them. Use the unitary method to find the difference in the cube roots of 830 and 833 for the difference of 10 between them. Finally, add the obtained difference with the cube root of 830 to get the answer.

$\Rightarrow 830 < 833 < 840$
$\Rightarrow {{\left( 830 \right)}^{\dfrac{1}{3}}} < {{\left( 833 \right)}^{\dfrac{1}{3}}} < {{\left( 840 \right)}^{\dfrac{1}{3}}}$
Now, using the cube root table we have the values ${{\left( 830 \right)}^{\dfrac{1}{3}}}=9.398$ and ${{\left( 840 \right)}^{\dfrac{1}{3}}}=9.435$, so we get,
$\Rightarrow 9.398 < {{\left( 833 \right)}^{\dfrac{1}{3}}} < 9.435$
\begin{align} & \Rightarrow {{\left( 833 \right)}^{\dfrac{1}{3}}}-{{\left( 830 \right)}^{\dfrac{1}{3}}}=\dfrac{0.037}{10}\times 3 \\ & \Rightarrow {{\left( 833 \right)}^{\dfrac{1}{3}}}-9.398=0.0111 \\ & \Rightarrow {{\left( 833 \right)}^{\dfrac{1}{3}}}=9.4091 \\ \end{align}
$\therefore {{\left( 833 \right)}^{\dfrac{1}{3}}}=9.409$
Note: When you observe the cube root table you will observe certain columns. In the first column we have certain numbers represented as x, in the second column we have the value ${{\left( x \right)}^{\dfrac{1}{3}}}$, in the third column we have ${{\left( 10x \right)}^{\dfrac{1}{3}}}$ and in the fourth column we have ${{\left( 100x \right)}^{\dfrac{1}{3}}}$. From here you may think about the reason for considering the relation 830 < 833 < 840. We can find the values of cube roots of 10 times and 100 times a number from the cube root table directly and not a number which does not end with the digit 0 like 833.