Posted by Sue Bonds on .
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,
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(325) = 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).