Simplify radicals? Can anyone help?

Question

Please help me with all you can, thanks. The first person to get all 5 right gets 10pts! I promise.

1. √3*√27

2. √15*√3+√15*2√5

3. 4√3+√12

4. √80x+2√45x-3√20x

5. √49x^2

Answer 1

1. 9

2. 3sqrt(5) + 10sqrt(3)

3. 6sqrt(3)

4. 4sqrt(5x)

5. 7x

Answer 2

The thing you need to know to do these problems is: √(a*b) = √a * √b. That and looking for where you can factor out perfect squares.

1. √3*√27 = √(3*27) = √81 = 9

2. √15*√3+√15*2√5 =
√(45) + 2√(75) =
√(9*5) + 2√(25*3) =
√9*√5 + 2√25*√3 =
3√5 + 10√3

3. 4√3 + √12 =
4√3 + √(4*3) =
4√3 + √4*√3 =
4√3 + 2√3 =
6√3

4. √80x+2√45x-3√20x =
√(16*5)x + 2√(9*5)x - 3√(4*5)x =
√16√5x + 2√9√5x - 3√4√5x =
4√5x + 6√5x - 6√5x =
4√5x
(if x is outside the radical, it's 4√5 * x, otherwise it's 4√(5x))

5. √49x^2
7x^2 (If you mean "√49 * x^2")
7x (if you mean √(49x^2))

The little radical signs are cute, but without parentheses, it is difficult to tell where you want the radical to stop. There's a difference between (√5) * x and √(5x)... but both seem to be written √5x.

Answer 3

1. √3*√27
9
2. √15*√3+√15*2√5
9√5
3. 4√3+√12
4√3+√4* √3
4√3+2√3
6√3
4. √80x+2√45x-3√20x
√16*5x+2√9*5x-3√4*5x
4√5x+6√5x-6√5x
4√5x

5. √49x^2
√7*7*x*x
7x

Answer 4

these are probally all wrong....
but it was worth a shot.
√3*√27=8.9999999

√15*√3+√15*2√5=52.905935

4√3+√12=6.04641016

√80x+2√45x-3√20x=4.4721359

√49x^2=14

Answer 5

1) 27= 3^3
therefore (27)^1/2 = 3^(3/2)
now 3^(1/2) * 3^(3/2) = 3^(4/2) = 3^2= 9

2) 15^(1/2) =5^(1/2) * 3^(1/2)
therefore the problem now becomes
[5^(1/2) * 3^(1/2)] *3^(1/2) + [5^(1/2) * 3^(1/2)]*(2*5^(1/2))
=> 5^(1/2) * 3 + 2*5*3^(1/2)
=> 3*5^(1/2) + 10*3^(1/2)

3) 12^(1/2) = 2*3^(1/2)
therefore the problem now becomes
4*3^(1/2) + 2*3^(1/2)
=> 6*3^(1/2)

4) 80^(1/2) = 4*5^(1/2)
45^(1/2) = 3*5^(1/2)
20^(1/2) = 2*5^(1/2)
therefore the problem now becomes
4*5^(1/2)x + 2*3*5^(1/2)x - 3*2*5^(1/2)
=> 4*5^(1/2)x

5) (49x^2)(1/2) = 7x

Answer 6

Wow buddy you should ask someone in your class so you actually get the concept instead of finding quick answers.