Question

Solve: sqrt 6x+5=sqrt 53

Answer 1

\[\sqrt{6x+5}=\sqrt{53}\]

Answer 2

Square both sides then solve for x.

Answer 3

Get it?

Answer 4

Not quite

Answer 5

\[(\sqrt{x})^2 = (x^{\frac{ 1 }{ 2 }})^2 = x^{\frac{ 2 }{ 2 }} = x^1 = x\]

Answer 6

Thus \( (\sqrt{6x+5})^2 = (\sqrt{53})^2 = 6x+5 = 53 \). Now solve for x.

Answer 7

If you square both sides, you will get this equation 6x+5=53. You should do this to make it easier to find the value of x.

Answer 8

thanks heaps! I understand now.

Answer 9

x=8?

Answer 10

@geerky42

Answer 11

What about this then? \[-4\sqrt{X+9}=20\]

Answer 12

Yes, x = 8. Now, for second problem, divide both sides by -4 to isolate radical. Once it is isolated, square both sides, just like we did in first problem.

Answer 13

\[\sqrt{x+9}/4\]=-5

Answer 14

-4*

Answer 15

Not what I mean. Here, let me show you.

\[-4\sqrt{x + 9} = 20\]Divide both sides by -4\[\dfrac{-4\sqrt{x + 9}}{-4} = \dfrac{20}{-4}\]\[\sqrt{x + 9} = -5\]Now square both sides.\[(\sqrt{x + 9})^2 = (-5)^2\]\[x+9 = 25\]
Is this clear?

Answer 16

oh on the left the -4 cancels out.. alright! and i see now! when squaring something it takes the radical away?

Answer 17

x=16

Answer 18

Well, to be exactly, if you square a square root, it will disappear. If you square a cubic root, it won't. And yes, x = 16. Is this clear? Do you need any more help?

Answer 19

Not at this moment! I appreciate your help very much. Much obliged. I will be sure to contact you with further questions!

Answer 20

Glad I helped!