# Algebra 2 TEST 7.1-7.5 PRACTICE SOLUTION

Views:

Category: Education

## Presentation Description

No description available.

## Presentation Transcript

### Algebra 2 TEST 7.1–7.5PRACTICE :

Algebra 2 TEST 7.1–7.5PRACTICE Solutions!

### 1 :

1 Find all the real-number roots. Note: There are two square roots of 0.16, namely 0.4 and –0.4. However, the radical sign is the principle root—the positive root whenever there is a choice!

### 2 :

2 Find all the real-number roots. No real solution. Neither a positive number squared nor a negative number squared gives a negative. There is no real number root to a negative number like –81.

### 3 :

3 Find all the real-number roots. On your calculator type:

### 4 :

4 Simplify each radical expression. Use absolute value symbols if needed. Note: If a radical has an even index (here 4) then the absolute value bars are needed. However, since both 2 and a2 are always positive, they may be removed from the absolute value bars.

### 5 :

5 Simplify each radical expression. Use absolute value symbols if needed. Note: Cube roots have only one answer. There is no need to choose between a positive and a negative value. Therefore, no absolute value bars should be used here.

### 6 :

6 Simplify each radical expression. Use absolute value symbols if needed.

### 7 :

7 Multiply and simplify if possible.

### 8 :

8 Multiply and simplify if possible. There are no real number square roots of a negative number (here –6). This problem has no real number solution.

### 9 :

9 Multiply and simplify if possible.

10 Multiply.

11 Multiply.

### 12 :

12 Multiply. Note: Usually we would FOIL the first line. With conjugates the outside and inside terms always cancel. FOIL reduces to simply FL.

### 13 :

13 Simplify. Assume that all variables are positive.

### 14 :

14 Simplify. Assume that all variables are positive. Note: If we “assume that the variables are positive” then absolute value bars are not needed.

### 15 :

15 Multiply and simplify. Assume that all variables are positive.

### 16 :

16 Multiply and simplify. Assume that all variables are positive.

### 17 :

17 Divide and simplify.

### 18 :

18 Divide and simplify.

### 19 :

19 Divide and simplify. Assume that all variable are positive.

### 20 :

20 Divide and simplify. Assume that all variable are positive.

### 21 :

21 Rationalize the denominator of the expression. Assume that all variables are positive. Comment: This is a killer problem!

### 22 :

22 Rationalize the denominator of the expression. Assume that all variables are positive.

### 23 :

23 Rationalize the denominator of the expression. Assume that all variables are positive. Note: FOIL on top; FL on bottom!

### 25 :

25 Add or subtract if possible. Simplify all answers. Note: This problem cannot be simplified any further. The radicands are different.

27 Simplify.

28 Simplify.

29 Simplify.

30 Simplify.

### 31 :

31 Write the following in radical form.

### 32 :

32 Write the following in radical form.

### 33 :

33 Write in simplest form.

### 34 :

34 Solve and check for extraneous roots.

### 35 (method 1) :

35 (method 1) Solve and check for extraneous roots. Note: Both answers check!

### 35 (method 2) :

35 (method 2) Solve and check for extraneous roots. Note: Both answers check!

### 36 :

36 Solve and check for extraneous roots. Note: –6 fails in the original. Extraneous!