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!