CPhill

(√2+5)(√10-4)

OK...so we have

√2*√10 - 4√2 + 5√10 - 20  =

√20 - 4√2 + 5√10 - 20 =

2√5 - 4√2 + 5√10 - 20

And that's as much as we can simplify this.

32)   So, I assume we have  3*3√5y^3* 2*3√50y^4  ???

9√5y^3 * 6√50y^4

9√5y^3 * 6√(25*2)y^4

9√5y^3 * 6*5√(2)y^4

9√5y^3 * 30√(2)y^4

270(y^7)√10

I did   5)  after 30....that's the one between the lines....I look at 32 in a sec !!!

Let's convert -(1 + 2/3)  to an "improper" fraction  = -5/3

Now, let's multiply...

(3/5) (-5/3)  =  (-15/15)  = -1

Not too bad, huh??

Here's a pretty good page that explains it all.......(I can't add anything, so I won't !!!)

Notice that we can carry Melody's answer one step more.....

(5x - 15) / (x -3)  =

5(x - 3) / (x - 3) =

5   ......    (with the restriction that x≠ 3)

28) 3√6* 3√16

So we have

 3√6 * 3*4  =    note that we are just multiplying now, Nataszaa

3*3*4*√6 =

36√6    ...we can't do anything with the square root of 6 !!! 

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30) √8x^5*√3x   =  √(2*2*2)x^5*√(3)x = √(4*2)x^5*√(3)x = 2√(2)x^5*√(3)x =

2* x^5 * x * √(2) * √(3)  =  (2x^6)√(6)

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3√7x/3√5y^2 = (the 3's "cancel) = √7x/√5y^2= (Multiply the numerator and denominator by √5) =  (√35x)/(5y^2)

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Nataszaa, repost 32 again.......are there some parenthesis involved???

We can use scientific notation here:

[ 1.5 x 10¹² ] / [ 7 x 10⁹ ] = [ 15 x 10¹¹ ] / [ 7 x 10⁹ ] ≈ 2.1428 x 10² ≈ $ 214.28

Note 5√2048  =  5*[2⁵ √2] = 5 [32 √2] = 160√2

I assume 5^5√2 is supposed to be  (5^5)√2 =  3125√2

So we have  160√2 + 3125√2  =  3285√2