1. ## square roots

Hi are my answers correct on these problems? If not can some one show me the correct process. Thanks Very Much!!

simplify:
sqrt45 + 5sqrt5 + sqrt20

I got 10sqrt5 as my answer.

and
solve for x
______
\/ x+9 = 3-x

i got x= 0,5
Thanks

2. The idea is to find out which square root all the terms can be factored into, then you usually end up with the square root of a perfect square (an integer that is the square of another integer). Then you can take the square root of that perfect square (for each term) and you get multiples of the same square root that you can add together. In this question, the second term already has the first couple steps done, so it gives you a hint of what square root to convert the others into.

sqrt45 + 5sqrt5 + sqrt20
= sqrt(9)*sqrt(5) + 5*sqrt(5) + sqrt(4)*sqrt(5)
=3sqrt(5)+5sqrt(5)+2sqrt(5)
=10sqrt(5)

I don't understand what the capital V stands for, but assuming the following equation is the one you need to solve, then the solution is as follows:
x+9=3-x
x+x+9=3
2x=-6
x=-3

3. Hello, celebciti!

. . . . . . . . .__ . . . ._ . . . __
Simplify: . √45 + 5√5 + √20
. . . . . . ._
I got 10√5 as my answer . Good!

. . - . . - . . . ._____
Solve for x: .√x + 9 .= .3 - x

i got x = 0.5 . . . . no
. . . . . . . . . . . . . . . .____
Square both sides: .(√x + 9)² .= .(3 - x)²

. . and we have: .x + 9 .= .9 - 6x + x²

. . and the quadratic: .x² - 7x .= .0

. . which factors: .x(x - 7) .= .0

. . and has two roots: .x .= .0, 7

We must check our answers . . .

Check x = 7. . . . . . . . . . . . . . . . _____ . . . __
The left side of the equation is: .√7 + 9 .= .√16 .= .4
The right side of the equation is: .3 - 7 .= .-4
. . The answer does not check . . . x = 7 is an extraneous root.

Check x = 0. . - . ._____
The left side is: .√0 + 9 .= .3
The right side is: .3 - 0 .= .3
. . The answer checks . . . x = 0 is a root.

4. Thanks So Much!