Answer:
A. 4 (RootIndex 3 StartRoot 7 x EndRoot) or ![4(\sqrt[3]{7x})](https://tex.z-dn.net/?f=4%28%5Csqrt%5B3%5D%7B7x%7D%29)
Step-by-step explanation:
Given:
A radical whose value is, ![r_1=\sqrt[3]{7x}](https://tex.z-dn.net/?f=r_1%3D%5Csqrt%5B3%5D%7B7x%7D)
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
![r_1 = n \times r_2 ](https://tex.z-dn.net/?f=r_1%20%3D%20n%20%5Ctimes%20r_2%0A)
Where, 'n' is a real number.
Here, ![r_1=\sqrt[3]{7x}](https://tex.z-dn.net/?f=r_1%3D%5Csqrt%5B3%5D%7B7x%7D)
Now, let us check all the options
.
Option A:
4 (RootIndex 3 StartRoot 7 x EndRoot) or ![r_2=4\sqrt[3]{7x}](https://tex.z-dn.net/?f=r_2%3D4%5Csqrt%5B3%5D%7B7x%7D)
Now, we observe that
is a multiple of
because
![r_2=4\times \sqrt[3]{7x}\\\\ r_2=4\times r_1..............(r_1=\sqrt[3]{7x})](https://tex.z-dn.net/?f=r_2%3D4%5Ctimes%20%5Csqrt%5B3%5D%7B7x%7D%5C%5C%5C%5C%20r_2%3D4%5Ctimes%20r_1..............%28r_1%3D%5Csqrt%5B3%5D%7B7x%7D%29)
Therefore, option A is correct.
Option B:
StartRoot 7 x EndRoot or ![r_2=\sqrt{7x}](https://tex.z-dn.net/?f=r_2%3D%5Csqrt%7B7x%7D)
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 ![r_2=x\sqrt[3]{7}](https://tex.z-dn.net/?f=r_2%3Dx%5Csqrt%5B3%5D%7B7%7D)
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 ![r_2=7\sqrt{x}](https://tex.z-dn.net/?f=r_2%3D7%5Csqrt%7Bx%7D)
As the above radical is square root and not a cubic root, this option is incorrect.
Therefore, the like radical is option (A) only.