Question

How do you determine the cube root of $36$.

Answer 1

Hint: Here, in the given question, we need to determine the cube root of $36$. When we say the cubed root of $36$, then it would mean $46,656$. This is calculated as $36 \times 36 \times 36$. But the cube root of $36$ means $\sqrt[3]{{36}}$. We will first find the factors of $36$ in exponential form. After this, we will find the cube root of the factors and find the solution for the cube root of $36$.

Complete step by step answer:
Factors of $36$ in exponential form can be given as,
$ \Rightarrow 36 = 2 \times 2 \times 3 \times 3$
Now we will take cube root of the above equation, we get
$ \Rightarrow \sqrt[3]{{36}} = \sqrt[3]{{2 \times 2 \times 3 \times 3}}$
It can also be written as,
$ \Rightarrow \sqrt[3]{{36}} = \sqrt[3]{{{2^2} \times {3^2}}}$
$ \Rightarrow \sqrt[3]{{36}} = \sqrt[3]{{{2^2}}} \times \sqrt[3]{{{3^2}}}$

On squaring inside the radical, we get
$ \Rightarrow \sqrt[3]{{36}} = \sqrt[3]{4} \times \sqrt[3]{9}$
As we know, the value of $\sqrt[3]{4}$ is $1.587$ and $\sqrt[3]{9}$ is $2.080$, putting these values in the above equation, we get
$ \Rightarrow \sqrt[3]{{36}} = 1.587 \times 2.080$
On multiplication, we get
$ \therefore \sqrt[3]{{36}} = 3.30096$

Therefore, the cube root of $36$ is $3.30096$.

Additional information: Remember that cube root of $36$ can be represented as ${\left( {36} \right)^{\dfrac{1}{3}}}$ and $\sqrt[3]{{36}}$. In $\sqrt[3]{{36}}$, the symbol $\sqrt {} $, is called the radical sign, $36$ is the radicand (it is the number below the radical sign), and $3$ is the index.

Note: Students should do the proper factorization of the given number. Students should know the cube root of basic small numbers. Remember that writing four numbers after the decimal point is enough. Students are not supposed to write all the numbers after the decimal point. Below is a tabular form for the cube root of numbers from $1$ to $10$.

Number	Cube root $\sqrt[3]{n}$
$1$	$1.000$
$2$	$1.260$
$3$	$1.442$
$4$	$1.587$
$5$	$1.710$
$6$	$1.817$
$7$	$1.913$
$8$	$2.000$
$9$	$2.080$
$10$	$2.154$