Making use of the cube root table, ____is the cube root of 8.65 correct to three decimal places.

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Detailed Solution

Here we are asked to find the cube root of the number 8.65
So we have

\sqrt[3]{8.65}

Now we will write this number 8.65 in fractional form, which will be equal to

\frac{865}{100}

\sqrt[3]{8.65} = \sqrt[3]{\frac{865}{100}}

Let’s find the cube root of 100

\sqrt[3]{100} = 4.642

Now, we have 860 < 865 < 870
So, let’s find the cube roots of three of them individually

\Rightarrow \sqrt[3]{860} = 9.510 - - (1)

Then let’s find the roots of 870

\sqrt[3]{870} = 9.546 - - - - (2)

Now we will try to find the difference in values of (1) and (2)
Difference in values  = 870−860 = 10
Now we will find the difference in cube roots values
Difference in cube roots value  = 9.546−9.510 = 0.036
Similarly we will do it for 865 and 860 respectively
Difference between values  =865−860=5
Difference in cube roots values =100.036×5=0.018