maths surds please help and explain

Simplify

A.1/root a +2
b.root 18/25
c.root a x cubed root a
d.root x + 2 root y/root x-2 root y
e.root5 x root72 /root 3

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asked by Bettina
  1. you really have to use brackets to establish the order of operations you want.

    e.g. in #1,
    the way you typed it it would be (1/√a) + 2
    but I sense you meant 1/(√a + 2)

    in b) did you mean √(18/25) ?

    etc

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    posted by Reiny
  2. e) is the only one not ambiguous,

    √5*(√72/√3)
    = √5*√24
    = √120
    = 2√30

    Also your use of x is not consistent
    in c) you are using x as a multiplier, in d) you are using x as a variable
    if you have to show a multiplication signs, either use brackets such as (2)(3) or the * sign,
    eg 2*3

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    posted by Reiny
  3. Key
    *=multiplication
    |= square root because I don't have the correct symbol

    A.1/|a +2
    b.|18/25
    c.|a * 3|a
    d.|x + 2|y / |x - 2|y

    Please help

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    posted by Bettina
  4. Ok, so you are saying
    a. 1/√a + 2
    = (1/√a)(√a/√a) + 2
    = (√a)/a + 2

    b. still not clear if you meant
    √(18/25) or √18 /25
    for first interpretation: = 3√2/5
    for 2nd interpretation: = 3√2 /25

    c). I will take the original as
    squareroot(a) * cuberoot(a)
    = a^(1/2) * a^(1/3)
    = a^(1/2+1/3)
    = a^(5/6) or (sixthroot(a))^5

    d) again, I will read it as

    y√(x+2)/(y√(x-2) )
    = √(x+2)/√(x-2)
    = √(x+2)/√(x-2) * √(x-2)/√(x-2)
    = √((x+2)(x-2) )/(x-2)
    = √(x^2 - 4)/(x-2)

    the second line of √(x+2)/√(x-2) should be accepted as simplified as well, unless it wanted the denominator rationalized

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    posted by Reiny
  5. Thanks alot reiny

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    posted by Bettina

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