
What is the cube root of -216?
Answer
450.6k+ views
Hint: Cube root of a number is a value which when multiplied by itself thrice or three times produces the original value. To find the cube root of -216, that is, , we have to split this as . By using , we can write . We have to find the cube root of -1 and 216 separately and substitute it in this form.
Complete step by step solution:
We have to find the cube root of -216. We know that the cube root of a number is a value which when multiplied by itself thrice or three times produces the original value. Cube root is denoted as . Let us consider the cube root of , that is, . We know that . Hence, the cube root of will be m.
Now, let us consider . We can write this as .
We know that . Hence, we can write as
Let us first find the cube root of -1. We know that . Therefore, we can write
Now, let us find the cube root of 216. For this, let us find the prime factors of 216.
We can write 216 as . We have to combine each triple.
Hence, we can write .
Let us substitute (ii) and (iii) in (i).
Hence, the cube root of -216 is -6.
Note: Students must know the properties of roots and how to find the prime factors of 216. We can also denote cube root of a number, say m, as m to the power of or .
Therefore, we can write .
Complete step by step solution:
We have to find the cube root of -216. We know that the cube root of a number is a value which when multiplied by itself thrice or three times produces the original value. Cube root is denoted as
Now, let us consider
We know that
Let us first find the cube root of -1. We know that
Now, let us find the cube root of 216. For this, let us find the prime factors of 216.
We can write 216 as
Hence, we can write
Let us substitute (ii) and (iii) in (i).
Hence, the cube root of -216 is -6.
Note: Students must know the properties of roots and how to find the prime factors of 216. We can also denote cube root of a number, say m, as m to the power of
Therefore, we can write
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