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Answer:
A. 4 (RootIndex 3 StartRoot 7 x EndRoot) or
Step-by-step explanation:
Given:
A radical whose value is,
Now, we need to find the like radical for .
Let the like radical be .
As per the definition of like radicals, like radicals are those that can be expressed as multiples of each other.
So, if two radicals are like radicals, then
Where, 'n' is a real number.
Here,
Now, let us check all the options .
Option A:
4 (RootIndex 3 StartRoot 7 x EndRoot) or
Now, we observe that is a multiple of
because
Therefore, option A is correct.
Option B:
StartRoot 7 x EndRoot or
As the above radical is square root and not a cubic root, this option is incorrect.
Option C:
x (RootIndex 3 StartRoot 7 EndRoot) or
As the term inside the cubic root is not same as that of , this option is also incorrect.
Option D:
7 StartRoot x EndRoot or
As the above radical is square root and not a cubic root, this option is incorrect.
Therefore, the like radical is option (A) only.