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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 :10 Multiply.
11 :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!
24 :24 Add or subtract if possible. Simplify all answers.
25 :25 Add or subtract if possible. Simplify all answers. Note: This problem cannot be simplified any further. The radicands are different.
26 :26 Add or subtract if possible. Simplify all answers.
27 :27 Simplify.
28 :28 Simplify.
29 :29 Simplify.
30 :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!