√x+1=5

Question

√x+1=5

anonymous · Answer

is that
$\large \sqrt {x+1}=5 $      OR   $\large \sqrt x +1=5$    ???

anonymous · Answer

the second one

whpalmer4 · Answer

$$\sqrt{x}+1=5$$Subtract 1 from each side
$$\sqrt{x}=4$$A definition of the square root is 
$$\sqrt{x}*\sqrt{x} = x$$What number times itself gives you 4?

anonymous · Answer

2

whpalmer4 · Answer

Yes, 2 is the square root of 4.  But we don't want that, we want to go the other way!

What number is 4*4?  4 is the square root of x.

anonymous · Answer

16?

whpalmer4 · Answer

Right!  Now if we plug 16 in for x in our equation, we have
$$\sqrt{16}+1 =5$$but we know that $4=\sqrt{16}$ so that becomes $$4+1=5$$and our work is done.  $x=16$

whpalmer4 · Answer

We get their algebraically by 
$$\sqrt{x} = 4$$Square both sides of the equation:
$$\sqrt{x}*\sqrt{x} = 4^2$$$$x = 16$$

whpalmer4 · Answer

We get *there*, sigh.

anonymous · Answer

thanks so much!

whpalmer4 · Answer

Let's do another one: we'll do the other problem that this might have been.

$$\sqrt{x+1} = 5$$How do you think we should start?

anonymous · Answer

would you subtract 5 from each side?

whpalmer4 · Answer

No, that wouldn't help.  How about something else?  One of the steps we used on the previous problem.

whpalmer4 · Answer

In the previous problem, we subtracted 1 from each side to the get the quantity under the square root (aka radical) sign all by itself prior to  ____________________ (your answer goes here)

anonymous · Answer

well i have another problem i really need help with

whpalmer4 · Answer

okay, we'll look at that next, but this is important, too.

anonymous · Answer

ok

whpalmer4 · Answer

the answer I'm looking for is "square both sides"

$$\sqrt{x+1}\sqrt{x+1} = 5*5$$Now what?

whpalmer4 · Answer

Well, the square root of something * the square root of that same something is just the something.  That gives us
$$x+1 = 25$$What is the value of $x$?

anonymous · Answer

25?

whpalmer4 · Answer

Does 25 + 1 = 25?

whpalmer4 · Answer

$$x+1=25$$Subtract 1 from both sides to isolate $x$
$$x+1-1=25-1$$$$x=24$$

Plugging our value back into the original equation
$$\sqrt{24+1}=5$$$$\sqrt{25} = 5$$because $5*5=25$so our answer is correct.

Now, let's see that other problem of yours!

anonymous · Answer

oh ok. 2√x+3=10

whpalmer4 · Answer

Is that $$2\sqrt{x}+3=10$$ or $$2\sqrt{x+3}=10$$?

anonymous · Answer

the second one

whpalmer4 · Answer

I wonder where my post went?  I did the first one, figuring it *wasn't* the one you had to do.  @#$@#% OpenStudy.

Okay, I would suggest you start your problem by squaring both sides.  That's generally a good plan when you have a radical sign on one side without any other terms added on.  You could also start by dividing both sides by 2, then squaring both sides.  You'll get the same result, numbers will be smaller to work with, but sometimes you end up with fractions (as in the first one).