Oh! One More Thing!

[ProfessorFilostrato]

I know, I know, I'm abusing this board now and waring out my welcome. But, I have a math final on Tuesday and I wanna make sure I know this stuff. So, if someone could help me check tis I'd be much happy!
[sqrt]18 + [sqrt]50

I got [sqrt]68 as my answer.

 

[tkhunny]

[sqrt]18 + [sqrt]50
I got [sqrt]68 as my answer.

Ouch! There is no such thing as the Distributive Property of Square Roots over Addition, though many, many beginning algebra students have tried it. Never do that again.

Prime factorization and look for perfect squares. There are NO shortcuts.

sqrt(18) = sqrt(9*2) = sqrt(2*3^2) = 3*sqrt(2)
sqrt(50) = sqrt(25*2) = sqrt(2*5^2) = 5*sqrt(2)

So,

sqrt(18) + sqrt(50) = 3*sqrt(2) + 5*sqrt(2) = [sqrt(2)]*(3+5) = 8*sqrt(2)

 

[soroban]

Hello, ProfessorFilostrato!

You're not abusing the board . . . but are we wasting our time?
You don't see to be <u>learning</u> anything from us ... We're just doing your homework!

[sqrt](18) + [sqrt](50)

I got [sqrt]68 as my answer. no! . . . If it was that easy, why assign homework?

Okay . . . one more time . . .

To simplify a radical, factor the number into two parts, one of which is a <u>square</u>, if possible.

We have: .[sqrt](18) . . 18 = 3 x 6 (but neither is a square).
. . . But: .18 = 9 x 2 (and 9 is a square!)
. . . . . . . . . . __ . . . . .___ . . . . _ . _ . . . . . ._
We write: . √18 . = . √9·2 . = . √9·√2 . = . 3√2
. . . . . . . . . . . . . .__ . . . . .____ . . . . __ . _ . . . . . ._
We also have: . √50 . = . √25·2 . = . √25·√2 . = . 5√2
. . . . . . . . . . . . . . . . . . _ . . . . _
Now we <u>add</u> them: . 3√2 + 5√2.

. . [Now after all this work, don't go weird on me!]
. . This is <u>exactly</u> like combining: .3X + 5X .= .8X . . . got it?
. . . . . . . . . . _
Answer: . 8√2