Question

Which of the following is a radical equation?

Answer 1

The condition for an equation to be a Radical Equation (or Irrational Equation) is that the value we are looking for (this means the variable of the equation) must be under a radical (inside a root $\sqrt{}$ sign).

Now, according to this, the only equation that fulfills this condition is c, because its variable $x$ is under a radical:

$\sqrt{x+3}=13$

The others, as we can see, don’t have the variable under a radical:

a) $x\sqrt{3}=13$

b) $x+\sqrt{3}=13$

d) $x+3=\sqrt{13}$

To solve this radical equation, we have to square both sides the equation:

${\sqrt{x+3}}^{2}=13^{2}$

$x+3=169$

$x=169-3$

$x=166$

Answer 2

The answer for this question is C. 
First subtract the 3 from both sides to get : sqrt(x) = 10
Then square both sides to get: x = 100
The other equations can't simply proving that they cannot be radical equations
Hope this helps :)