Question

What is the cube root of 72?

Answer 1

Hint: Here in this problem we have to find the cube root of 72. The number 72 is not a perfect cube number. So we have to do some calculations and simplifications to get the solution. We can first separate the number into two terms inside the square root and further simplify it to get the final answer.

Complete step-by-step answer:
Here we have to find the cube root of 72.
To find the cube root of 72, now we can rewrite the 72 in the cube root form, where
\[= \sqrt[3]{72}\]
Since the number 72 is not a perfect cubic number. So now we can separate the number 72 that is,
\[= \sqrt[3]{8\times 9}\] where the multiplication of \[8\times 9=72\]
Since looking for the perfect cube number, here 8 is perfect cube number so,
\[= \sqrt[3]{{{2}^{3}}\times {{3}^{2}}}\]
Now we can separate the cube root for the multiplication numbers, we get
\[= \sqrt[3]{{{2}^{3}}}\times \sqrt[3]{{{3}^{2}}}\]
Now simplifying the perfect cube number and taking it out of the cube root,
\[= 2\sqrt[3]{{{3}^{2}}}\]
Where 9 is not a perfect cube number so we can keep it as it is or \[{{3}^{2}}\].
Therefore, the cube root of 72 is \[2\sqrt[3]{{{3}^{2}}}\].

Note: These types of problems have slightly difficult to separate the given number to get multiplied and finding the perfect cube number if the given number is a non -cubic number. The above solved problem can be solved through another method also using a scientific calculator. The scientific calculator value is 4.1061676461. Here we should be careful while separating the non- cubic number. Students can make careless mistakes in it.