Math Help Me Again Please!?

Question

Solve the equations and show the work:

a) √x -1 = 3

b) √x^3 = 8

c) 3^√x^2 = 4

Answer 1

To get rid of a square root, you need to get the square root expression alone, then square both sides...

a) √x -1 = 3
Is this
(√x) -1 = 3
or
√(x -1) = 3

If it's
(√x) -1 = 3
(√x) = 4
x = 16

If it's
√(x -1) = 3
x - 1 = 9
x = 10


b) √x^3 = 8
x^3 = 64
x^3 = 4^3
x = 4


c) 3^√x^2 = 4
Is that "third root of x^2"??
If so, then cube both sides...
x^2 = 4^3
x^2 = 64
x = 8 or -8

Answer 2

a) √x -1 = 3
SOLUTION: I'm not sure whether you meant √(x -1) = 3 or (√x) -1 = 3. (Depends on whether the square root symbol covers everything on the left-side or just x). I'll just work both below:

(i)√(x -1) = 3
Square both sides:
(x-1) = 9
Add 1 to both sides:
x = 10

(ii) (√x) -1 = 3
Add 1 to both sides:
√x -1 + 1 = 3 + 1
√x = 4
Now square both sides:
(√x)^2 = (4)^2
x = 16

b) √x^3 = 8
SOLUTION:
√x^3 = 8
From the way you wrote it, this can be interpreted as (√x)^3 = 8 OR √(x^3) = 8
It doesn't matter though. We will use the first one as it is easier.
(√x)^3 = 8
Now, firstly take the cube root of both sides:
[(√x)^3]^(1/3) = (8)^(1/3)
(√x) = 2
So square both sides:
(√x)^2 = (2)^2
x = 4

c) 3^√x^2 = 4
I presume you mean cube root for the start:
So let's start by taking the cube of both sides to eliminate this cube root:
[3^√x^2]^3 = 4^3
x^2 = 64
Now take the square root of both sides to find x:
√x^2 = √64
x = 8 or x=-8
Why? Because whenever you square a number, both negatives and positives become positive. Therefore when you do the reverse (take the square root) you have to take into consideration that there could have been 2 numbers to give you that positive number.

NOTE: √x = (x)^(1/2)
and 3^√x = (x)^(1/3)

Answer 3

a) √x -1 = 3
=>√x = 3+1
=>√x = 4
=>x = 4^2
=>x = 16

b) √x^3 = 8
=> x^3 = 64
=> x = ³√64
=> x = 4

c) 3^√x^2 = 4.............not written properly

3*√x^2 = 4
9 x^2 = 16
x^2 = 16/9
x = ± 4/3
ans x = + 4/3 only

Or
³√x^2 = 4
=> x^2= 64
=> x = ± 8
ans x = + 8 only

Answer 4

a)
add 1 to both side:

sqrt(x)=4: square both sides
x=16

b)
this is rewritten:
x^(3/2)=8
do this ins parts:
square both sides:
x^3=64
now take the 3rd root: What times itself 3 times give you 64
x=4

c)
rewrite:
x^(2/3)=4
take the sqrt of both side:
x^(1/3)=2
now we have to cube both sides:
x=2*2*2=8
x=8

Answer 5

its not all 2

perhaps this helps -

√x -1 = 3
√x = 4
x=4^2
x=16

√x^3 = 8
x^3=8^2
x^3=64
x=(cube root)64
x=4

3^√x^2 = 4
x^2=4^3
x^2=64
x=√64
x=8, -8

Answer 6

a) 10

b) 4

c) 2

Answer 7

2.2.2 all of them are 2