# Math Help - Radical numbers

x-5-2=3
radical sign is under the x-5.

x= x+7+5
radical sign is under the x+7

Multiply

(36 +2)(4-63)

simplify
(9x)^2
Is that 3x?

-125c^3

Find the domain of the given function.
F(x)=2x-3
radical sign is under the 2x-3.

Thank you

2. Originally Posted by rowdy3
x-5-2=3
radical sign is under the x-5.

Thank you
The first two are similar here is the first

$\sqrt[3]{x-5}-2=3$ add two to both sides

$\sqrt[3]{x-5}=5$ cube both sides

$(\sqrt[3]{x-5})^3=5^3 \iff x-5=125 \iff x=130$

3. x= x+7+5
Would I subtract 5 from x? That would give me -5= x+7. I would square everything (-5)^2 = x=( x+7)^2. 25= x+7. I subtract 7 and get x=18.

4. Originally Posted by rowdy3
x= x+7+5
Would I subtract 5 from x? That would give me -5= x+7. I would square everything (-5)^2 = x=( x+7)^2. 25= x+7. I subtract 7 and get x=18.

$x=\sqrt{x+7}+5 \iff x-5=\sqrt{x+7}$ Now square both sides

$(x-5)^2=(\sqrt{x+7})^2 \iff x^2-10x+25=x+7$ collectin like terms

$x^2-11x+18=0 \iff (x-2)(x-9)=0$

So x=2 or x=9

we need to check both solutions to see if they work

plugging in 2 we get

$2 \overbrace{=}^{?} \sqrt{2+7}+5 \iff 2 \ne 3+5$

so 2 is Not a solution

if you check 9 it does work so it is the only solution

5. 2x+3 =9
(2x+3)^2 = (9)^2
2x+3=81
-3 -3
2x/2 = 78/2
x=39