1001 Algebra Problems.PDF

953. 3 +  6 = 3 + 6=  9 = 3
a.You must first simplify  6 as  6 = 2. 3
= 2 3 , and then combine with  3 to con-
clude that  3 +  6 = 3 3 .
b.The sum  3 +  6 cannot be simplified fur-
ther because the radicands are different.
c.There is no error.

954. 6 + ^3 –38= (2 +3)6 – 38= ^5 –32= –2
a.The calculation is correct until the last line;
the fifth root of a negative number is not
defined.
b.The first equality is incorrect: the radicals
cannot be combined since their indices are
different.
c.There is no error.

955. =  = =

= =

a.The third equality is incorrect because the

binomial was not squared correctly. The cor-

rect denominator should be 2^2 +2 3 +

( 3 )

2

= 7 + 2 3 .

b.The first equality is wrong because multiply-

ing by changes the value of the

expression. The rest of the equalities are

correct.

c.There is no error.

956.(x^5 )^2 = x^7 , for any real number x.
a.The exponents should be multiplied, not
added, so that the correct answer should be x^10.
b.The correct answer should be x^25 because
(x^5 )^2 = x^52.
c.There is no error.

957. ^3  27 x^3 = ^327 ^3 x^3 = 3x, for any real number
     x.
     a.The first equality is wrong because the radi-
     cal of a product is not the product of the
     radicals.
     b.The second equality holds only ifxis not
     negative because you can only take the cube
     root of a non-negative real number.
     c.There is no error.

958. = ^34 ^85 = ^65 

a.The first equality is wrong because you must

multiply the numerator by the reciprocalof

the denominator.

b.The second equality is wrong because the

fraction on the far right should be ^2240 , which

cannot be simplified further.

c.There is no error.

959. = x = x–4, for any non-negative real
     number x.
     a.The correct answer should be x^36 because
     = x^12 x^3 =x^12 ^3 =x^36.
     b.The correct answer should be x^15 because
     = x^12 x^3 =x12 + 3=x^15.
     c.There is no error.

960.(e^4 x)^2 = e^4 x+2

a.The correct answer should be e^8 xbecause

(e^4 x)^2 = e^4 x^2 = e^8 x.

b.The correct answer should be e^16 x^2 because

(e^4 x)^2 = e(4x)^2 = e^42 x^2 = e^16 x^2.

c.There is no error.

x^12

x–3

x^12

x–3

x^12 ^12 –3

x–3

^34 

^85 

2 + ^3 

2 +  3 

2 + ^3 

7

2 + ^3 

4 + 3

2 + ^3 

22 + ( 3 )^2

2 +^3 

(2 + 3 )^2

2 + ^3 

2 +  3 

^1

2 +  3 

^1

2 +  3 

• COMMON ALGEBRA ERRORS–