Respuesta :
Answer:
A. 4 (RootIndex 3 StartRoot 7 x EndRoot) or [tex]4(\sqrt[3]{7x})[/tex]
Step-by-step explanation:
Given:
A radical whose value is, [tex]r_1=\sqrt[3]{7x}[/tex]
Now, we need to find the like radical for [tex]r_1[/tex].
Let the like radical be [tex]r_2[/tex].
As per the definition of like radicals, like radicals are those that can be expressed as multiples of each other.
So, if two radicals [tex]r_1\ and\ r_2[/tex] are like radicals, then
[tex]r_1 = n \times r_2 [/tex]
Where, 'n' is a real number.
Here, [tex]r_1=\sqrt[3]{7x}[/tex]
Now, let us check all the options .
Option A:
4 (RootIndex 3 StartRoot 7 x EndRoot) or [tex]r_2=4\sqrt[3]{7x}[/tex]
Now, we observe that [tex]r_2[/tex] is a multiple of [tex]r_1[/tex] because
[tex]r_2=4\times \sqrt[3]{7x}\\\\ r_2=4\times r_1..............(r_1=\sqrt[3]{7x})[/tex]
Therefore, option A is correct.
Option B:
StartRoot 7 x EndRoot or [tex]r_2=\sqrt{7x}[/tex]
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 [tex]r_2=x\sqrt[3]{7}[/tex]
As the term inside the cubic root is not same as that of [tex]r_1[/tex], this option is also incorrect.
Option D:
7 StartRoot x EndRoot or [tex]r_2=7\sqrt{x}[/tex]
As the above radical is square root and not a cubic root, this option is incorrect.
Therefore, the like radical is option (A) only.
