Question

Making use of the cube root table, find the cube roots of the following (correct to three decimal places):
70

Answer 1

Hint: To find the cube root of 70 using the cube root table, first of all draw the cube root table. Now, we can write 70 as 7 multiplied by 10. Now, separate 7 and 10 under the radical sign. So, we need to look for $ x = 7 $ and $ x = 10 $ in the 1st column and then find its value corresponding to it in the 2nd column.

Complete step-by-step answer:
In this question, we are asked to find the cube root of 70 using the cube root table.
Cube root of a number means when we multiply that number thrice, we get the original number. Now, the cube root of a number can be found using multiple methods, but in this question, we are going to use the method of the cube root table.
For finding the cube root of 70 using the cube root table, let us first draw the cube root table.

$ x $	$ \sqrt[3]{x} $	$ \sqrt[3]{{10x}} $	$ \sqrt[3]{{100x}} $
1	1.000	2.154	4.642
2	1.260	2.714	5.848
3	1.442	3.107	6.694
4	1.587	3.420	7.368
5	1.710	3.684	7.937
6	1.817	3.915	8.434
7	1.913	4.121	8.379
8	2.000	4.309	9.283
9	2.020	4.481	9.655
10	2.154	4.642	10.000

Now, we need to find the cube root of 70. We can write 70 as 7 multiplied by 10. Therefore,
 $
   \Rightarrow \sqrt[3]{{70}} = \sqrt[3]{{7 \times 10}} \\
   \Rightarrow \sqrt[3]{{70}} = \sqrt[3]{7} \times \sqrt[3]{{10}} \;
  $
Now, here we have x as 7 and 10. So in the first column, we need to look for 7 and 10 and find the values in the 2nd column corresponding to that number.
So, for $ x = 7,\sqrt[3]{x} = 1.913 $ and for $ x = 10,\sqrt[3]{{10}} = 2.154 $
So, therefore the cube root of 70 will be
 $
   \Rightarrow \sqrt[3]{{70}} = \sqrt[3]{7} \times \sqrt[3]{{10}} \\
   \Rightarrow \sqrt[3]{{70}} = 1.913 \times 2.154 \\
   \Rightarrow \sqrt[3]{{70}} = 4.121 \;
  $
Hence, the cube root of 70 is 4.121
So, the correct answer is “4.121”.

Note: Here, instead of separating 7 and 10 under the radical sign we can also find the cube root by letting 7 as x and then looking for the value in the 3rd column.
 $ \Rightarrow \sqrt[3]{{70}} = \sqrt[3]{{10x}} $ , here $ x = 7 $
So, we look in the first column for 7 and then find its value corresponding to it in the 3rd column.
So, for $ x = 7 $ , $ \sqrt[3]{{10x}} = 4.121 $
Therefore,
 $ \Rightarrow \sqrt[3]{{70}} = \sqrt[3]{{10x}} = 4.121 $