Making use of the cube root table, find the cube roots of the following (correct to three decimal places):
70
Answer
280.2k+ 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
Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What is pollution? How many types of pollution? Define it

Scroll valve is present in a Respiratory system of class 11 biology CBSE

What is BLO What is the full form of BLO class 8 social science CBSE

is known as the Land of the Rising Sun A Japan B Norway class 8 social science CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

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

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
