Question

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

Answer 1

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).

Answer 2

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