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March 28, 2017

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1) Is the equation: 28 - 4√2 = 24√2 True? Explain why or why not?

2) Is this statement √a + √b = √(a +b) True? Explain why or why not?

3) What is the index of a radical? When working with radicals, can the radicand be negative when the index is odd? Can it be negative when the index is even?

4) Simplify the following expressions:-

(a) 8√48 - 5√3

(b) 7 * 3√(-16) + 15 * 3√2

  • Algebra - ,

    1. 28 - 4sqrt2 = 24sqrt2.
    24sqrt2 + 4sqrt2 = 28,
    28sqrt2 = 28. Not True.
    Divide both sides by 28:
    sqrt2 = 1. NOT TRUE.

    2. sqrt(a) and sqrt(b) can be added only if a = b. So the Eq is Not True.

    3. a. The index is 2 for a sqrt radical
    and 3 for a crt radical.
    b. Yes, the radican can be neg. when
    the index is odd.

    c. No, the radican cannot be neg. when the index is even.

    4a. 8sqrt48 - 5sqrt3 =
    8sqrt(16*3) - 5sqrt3 =
    8*4sqrt3 - 5sqrt3 =
    32sqrt3 - 5sqrt3 =
    Factor out 5sqrt3:
    sqrt3(32-5) = 27sqrt3.

    b. 21sqrt(-16) + 45sqrt2 =
    21sqrt(16*-1) + 45sqrt2 =
    21*4sqrt(-1) + 45sqrt2 =
    84sqrt(-1) + 45sqrt2 =
    Factor out 3:
    3(28sqrt(-1) + 15sqrt2 =
    3(28i + 15sqrt2).

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