Simplify and combine like radicals?

Question

√45 - √125

Answer 1

sqrt(45) - sqrt(125)

Your first step would be to decompose each of 45 and 125 into its prime factorization.

45 = 9 x 5 = 3 x 3 x 5, and
125 = 5 x 5 x 5

So now, you're taking

sqrt (3 x 3 x 5) - sqrt (5 x 5 x 5)

Every TWO repeated factors can be pulled outside the square root, and when they get pulled out, they become ONE. In the first case, we're pulling out two 3s, and on the outside they will become a single 3. Same thing with the two 5's. Everything else gets left inside the square root.

3sqrt(5) - 5sqrt(5)

Now, we can actually combine these. Subtracting these is no different than subtracting 3x - 5x.

-2sqrt(5)

Answer 2

√45 - √125 = (√9 - √25)√5 = (3 - 5)√5 = -2√5

Answer 3

First: simplify the numbers in the radicals:

V`(3*3*5) - V`(5*5*5)

Second: when you have a pair of the same number, take one out and place it in the front of the radical sign:

3 V`5 - 5 V`5

Third: you have the same square root > subtract coefficients:

-2 V`5

Answer 4

If we re-express each one :

45 | 5
.9. | 3
.3. | 3
.1. |

so √45 = 3√5

and

125 | 5
.25. | 5
..5.. | 5
..1.. |

√125 = 5√5

√45- √125 = 3√5 - 5√5

factorizing:

(3 - 5) √5 = -2√5

Answer 5

ok the 1st step is to place the sqrt's into easiest type, through taking away acceptable squares. to try this, you dived the quantity below the sqrt sign through acceptable squares, then you particularly take that sq. out. so sqrt32, 32 is divisible through sixteen (4^2) meaning 4*sqrt2 (32/sixteen=2) equals sqrt 32. so after simplifying, your sqrt's are: 4*sqrt2 7*sqrt2 6*sqrt2 now, all of those sqrt's have a typical element, sqrt2. so which you would be able to element that out so your project will become: sqrt2*(4+7+6) = sqrt2*(17) =17sqrt2, the terrific answer

Answer 6

3 sqrt 5 - 5 sqrt 5 = -2 sqrt 5

Answer 7

rt45=rt3*3*5
=3rt5
rt125=rt5*5*5
=5rt5
rt45-rt125=3rt5-5rt5
=-2rt5
=>-rt20