Making use of the cube root table, find the cube roots of the following (correct to three decimal places):
70
Last updated date: 20th Mar 2023
•
Total views: 205.2k
•
Views today: 4.84k
Answer
205.2k+ views
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.
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 $
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 $
Recently Updated Pages
If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts
What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?
