
Find the cube root of .
Answer
533.7k+ views
Hint: This question can be solved easily if we can write in the form of . Because it is easier to find the cube root, when it is represented as above.
Complete step-by-step answer:
We know that,
Now, we have to analyse the question and check whether it can be written in the form equation(i). We will first write the question in the form of equation (i). Then we will find the cube root.
According to the question we have to find the cube root of .
Now, we are going to simplify each term of the question
First, let us take and .
Here we can write as,
Similarly, we can write as,
Now, we can rewrite the question as,
Opening the brackets,
Rearranging the above equation to get the form of equation(i) we have,
Here can be written as . Similarly, can be written as .
Substituting this in equation (iv) we have,
Equation (v) we observe and .
Hence, equation (v) can be written in the form of equation (i) as follows,
Thus, from equation (vi) we observe that the question is rewritten in the form of equation (i).
Now, we can find the cube root.
Comparing equation (i) and equation (vi) we can simplify equation (vi) as,
Taking the cube root on both sides,
Hence, the cube root of is .
Note: The main idea is representing the problem in the form of,
. If this is correct then the student can easily simplify the above expression to obtain the cube root.
Complete step-by-step answer:
We know that,
Now, we have to analyse the question and check whether it can be written in the form equation(i). We will first write the question in the form of equation (i). Then we will find the cube root.
According to the question we have to find the cube root of
Now, we are going to simplify each term of the question
First, let us take
Here we can write
Similarly, we can write
Now, we can rewrite the question as,
Opening the brackets,
Rearranging the above equation to get the form of equation(i) we have,
Here
Substituting this in equation (iv) we have,
Equation (v) we observe
Hence, equation (v) can be written in the form of equation (i) as follows,
Thus, from equation (vi) we observe that the question is rewritten in the form of equation (i).
Now, we can find the cube root.
Comparing equation (i) and equation (vi) we can simplify equation (vi) as,
Taking the cube root on both sides,
Hence, the cube root of
Note: The main idea is representing the problem in the form of,
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