Posted by **Sue Bonds** on Saturday, August 6, 2011 at 9:12am.

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 -
**Henry**, Saturday, August 6, 2011 at 8:48pm
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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