Which of the following is a radical equation? x + StartRoot 5 EndRoot = 12 x squared = 16 3 + x StartRoot 7 EndRoot = 13 7 StartRoot x EndRoot = 14

The only radical equation is the last one : [tex]7\,\sqrt{x} =14[/tex], because it is the only one where the unknown appears inside the root. The name "radical equations" is associated with the fact that the unknown is contained inside the root and therefore the process involved in solving for the unknown will need to include the elimination of the root via algebraic methods to free the unknown.

Notice that the options a) and c) have roots, but what appears inside them are numbers (5 and 7 respectively), and not an unknown like "x". Equation b) doesn't contain a root, and wouldn't classify as a radical equation.

astha8579 astha8579 · Answer 2 · 2022-01-10T14:19:32+01:00

A radical equation is one which contains roots in it, specially those which has root over variables or things whose values changes.

Thus, by above definition, we will have the fourth option: [tex]7\sqrt{x} = 14[/tex] as a radical equation.

Given the equations:

[tex]x + \sqrt{5} = 12\\[/tex]

[tex]x^2 = 16[/tex]

[tex]3 + x\sqrt{7} = 13\\[/tex]

[tex]7\sqrt{x} = 14[/tex]

Explanation:

A radical equation is one which contains roots in it, specially those which has root over variables or things whose values changes.

Since only in the fourth option we see there's root over x which is a variable here, thus the fourth option: [tex]7\sqrt{x} = 14[/tex] is a radical equation.

Rest of the options, although containing roots, aren't having variables inside the root, thus they aren't classified as radical equations.

Learn more about radical equations here:

https://brainly.com/question/8606917