math questions?

Question

Simplify all radicals and combine:

1) 3 sq rt (square root) of 2 + 5 square root of 3 - 4 square root of 18

2) sq rt of 8 + sq rt of 32 - sq rt of 2

also

sq rt 128/sq rt 12

don't really need the answers as much as I need to know how to do these, all help appreciated, thanks.

Answer 1

for those 3 questions you can first....
1.) square all values
2.) solve
3.) you'll get a whole number
4.) then square root the whole number
5.) from there simplify

For example, for the first question you would get..
9(2) + 25(3) + 16(18)
=381
then take the square root...
....sqrt(381)
then just simplify a little bit further

hope this helped.....

Answer 2

1) 4 sq rt 18 is actually 12 sq rt 2 which can be combind w/
3sq rt 2 like this 5sq rt 3 - 9sq rt 2

2) the sq rt of 8 is 2sq rt 2 b/c 8= 2x2x2 (2 cubed)

128 sq rt 12 can be factored to 256 sq rt 3 b/c of the 4 in 12. sg rt of 4 is 2 so you multiply 128 by 2.

Answer 3

1) 3 sqrt(2) + 5sqrt(3) - 4sqrt(18). First, notice 18 factors into 2*3*3 (prime factors). There are two threes, so take out those two, and pull one to outside, so you have 4*3sqrt(2). Now, you have 3sqrt(2), 12sqrt(2), and 5sqrt(3). Combine the ones with sqrt(2), keeping in mind the signs.

2) sqrt(8) +sqrt(32)-sqrt(2). First, get the prime factors. 8=2*2*2, 32=2*2*2*2*2, 2=2. Now, pull out each pair, and keep only one on the outside. EX: sqrt(2*2*2) = 2sqrt(2). Do the same for 32. Then, combine the like terms, meaning in this case, the terms with sqrt(2). Add the whole number part, in this case 2, keeping signs.

3) sqrt(128)/sqrt(12). Factor primes, do same as previous example, dividing whole number parts.

Keep what is under sqrt... ex: sqrt(2). Do not add, subtract, divide, or multiply anything in the sqrt. Only bring out pairs.

Answer 4

1) 3 sq rt (square root) of 2 + 5 square root of 3 - 4 square root of 18
= 3sqrt(2) + 5sqrt(3) - 4sqrt(9*2)
= 3sqrt(2) +5sqrt(3) - 12sqrt(2)
= 5sqrt(3)-9sqrt(2)

2) sq rt of 8 + sq rt of 32 - sq rt of 2
= sqrt(4*2) +sqrt(16*2) -sqrt(2)
= 2sqrt(2) + 4sqrt(2) -sqrt(2)
= 5sqrt(2)

sq rt 128/sq rt 12
= sqrt(64*2)/sqrt(4*3)
=8sqrt(2)/2sqrt(3)
= 4sqrt(2)/sqrt(3)
= 4sqrt(6)/3

Answer 5

for these problems you have to factor the number inside the square root (i will use the notation sr #)

3 sr2 + 5 sr3 - 4 sr18 (factor 18)
3 sr2 + 5 sr3 - 4 sr(9*2) (now take the sr of 9 out & mult by 4)
3 sr2 + 5 sr3 - 12 sr2 (the 12 is from 3 * 4, 3 is sr of 9)
then combine like terms
-9 sr2 + 5 sr3 (sometimes it is easier to see the sr as a variable such as x then plug in at the end)

sr8 + sr32 - sr2
sr(4*2) + sr(16 * 2) - sr2
2 sr2 + 4 sr2 - sr2
5 sr2

sr128/sr12
sr(64*2)/sr(4*3)
8 sr2 / 2 sr3 (then simplify)
4 sr2/sr3

hope that helps