Question

The value of $64*{\left( { - 2744} \right)^{\dfrac{1}{3}}}$. is
a.56
b.-56
c.65
d.-65

Answer 1

Hint: As we are asked to find the product of $64*{\left( { - 2744} \right)^{\dfrac{1}{3}}}$. Using the BODMAS rule we solve the part in the brackets for which we need to find the cube root of -2744. We get that the cube root of - 2744 to be -14. And multiplying it with 64 we get the required product.

Complete step-by-step answer:
We are asked to find the value of the product $64*{\left( { - 2744} \right)^{\dfrac{1}{3}}}$
By using the BODMAS rule we give the first preference to the number in the brackets
So first let's find the cube root of $ - 2744$
We know that $ - 2744$ can be written as $ - 1*2744$
Hence, we get
$ \Rightarrow 64*{\left( { - 1*2744} \right)^{\dfrac{1}{3}}}$
From this we get that the cube root of $ - 1$is $ - 1$
And 2744 can be written as
$ \Rightarrow 2744 = 14*14*14$
Hence the cube root of 2744 is 14
Therefore we get
$
   \Rightarrow 64*\left( { - 1*14} \right) \\
   \Rightarrow 64* - 14 \\
   \Rightarrow - 896 \\
$
None of the options are correct

Additional information
Cube and cube root are inverse operations and hence cube root of the cube of a number is the number itself.
Cube root of a perfect cube number is always a whole number.
Prime factorization and estimation methods can be used to find the cube roots of perfect cubes only.

Note: Many students tend to find the cube root of 64 which is 4 and multiply it with -14 which gives us -56.
They may think it's correct as it's given in the options but here it's not necessary to find the cube root of 64 .