Question

Find the negative of the cube root of -2744000.

Answer 1

Hint: Reduce the given number -2744000 to power of its smaller factors or power of its prime factors, if required. Then for finding the cube root, divide those powers by 3. Take the negative of the number left after dividing the powers and it will be the answer.

Complete step-by-step answer:
According to the question, the given number is -2744000. We have to determine the negative of its cube root.
First we will find the cube root of -2744000. This number i.e. -2744000 can be written as the product of -1, 2744 and 1000. This is shown below:
$ \Rightarrow - 2744000 = - 1 \times 2744 \times 1000$
On dividing 2744 by 8, the result is 343. Thus 2744 can be written as the product of 343 and 8. Also 1000 can be written as 10 raise to the power 3 i.e. ${10^3}$. Substituting these values, we’ll get:
$ \Rightarrow - 2744000 = - 1 \times 8 \times 343 \times {10^3}$
Further, 8 is the cube of 2 i.e. ${2^3}$ and 343 is the cube of 7 i.e. ${7^3}$. Also -1 can be written as ${\left( { - 1} \right)^3}$. Substituting these values, we’ll get:
$ \Rightarrow - 2744000 = {\left( { - 1} \right)^3} \times {2^3} \times {7^3} \times {10^3}$
For finding the cube root, we’ll divide the powers by 3 on both sides. Doing this, we’ll get:
$
   \Rightarrow {\left( { - 2744000} \right)^{\dfrac{1}{3}}} = {\left( { - 1} \right)^{\dfrac{3}{3}}} \times {2^{\dfrac{3}{3}}} \times {7^{\dfrac{3}{3}}} \times {10^{\dfrac{3}{3}}} \\
   \Rightarrow \sqrt[3]{{ - 2744000}} = - 1 \times 2 \times 7 \times 10 \\
   \Rightarrow \sqrt[3]{{ - 2744000}} = - 140 \\
 $
Thus the cube root of -2744000 is -140. On taking the negative of it, we’ll get:
$ \Rightarrow - \sqrt[3]{{ - 2744000}} = 140$

Therefore the negative of cube root of -2744000 is 140.

Note: Here we have calculated the cube root of a negative number. But if we have to find the square root of a negative number, this will not give us a real value. In fact any even roots of a negative number will always be an imaginary number. And these roots are simplified using the value of iota i.e. $i = \sqrt { - 1} $.