MAT1033 EXAM 3 REVIEW ACTUAL UPDATED QUESTIONS AND CORRECT ANSWERS

MAT1033 EXAM 3 REVIEW ACTUAL UPDATED QUESTIONS AND CORRECT
ANSWERS

Exponents b^x=M ; 2^3=8 ; 2 x 2 x 2 = 8


Radicals: Radical Symbol
Index
Radicand




Find the Base 3^^√8= 2
Root of index 3 (cubic root) of 8 = 2




Root of Index 2 Called square root and # is not printed

, Square Root & Root of Index Examples 1) √25 = 5
2) √36 = 6
3) √x^2 = x
4) √x^4 = x^2
5) √x^3 = √x^2 * x = x√x
6) √x^7 = √x^6 * x = x^3√x
7) 3^^√x^3= x
8) 3^^√x^6 = x^2
9) 3^^√11 = 3^^√x^9x^2 = (x^3)3^^√x^2


In Depth Explanation EX1) 3^^√64 = 4 since 4^3 = 64
EX2) 3^^√-27 = -3 since (-3)^3= -27
EX3) 3^^√x^3 = x since x^3 = x^3
EX4) 3^^√(8/125) = (2/5) since (2/5)^3 = (8/125)
EX5) 3^^√-27x^9 = -3x^3 since (-3x^3)^3 = -27^9


Radical Expression Example 1 √(x^5)(y^6)(z^7)
= √(x^4)(x)(y^6)(z^6)(z)
=√(x^2)(y^3)(z^3)(3^^√xz)


Radical Expression Example 2 3^^√(x^7)(y^9)(x^10)
=3^^√(x^6)(x)(y^9)(z^9)(z)
=(x^y^3z^3)(^^3√xz)


Radical Expression Example 3 √8 = √4(2) = 2√2


Radical Expression Example 4 √50 = √25(2) = 5√2


Radical Expression Example 5 √300 = √100 (3) = 10√3


Radical Expression Example 6 √98 = √49(2) = 7√2




Multiplying Radical Expressions if the Index is the same EX1) √2 * √3 = √ 6
EX2) √2 * √X = √ 2x
EX3) √2 * √8 = √16 = 4


Multiplying Radical Expressions Example 1 √2x X √3x^3 X √18x = √108x^5
ALT1= √4(9)(3)(x^4)
= 6x^2√3x


ALT2: =√36(3)(x^4)x
=6x^2√3x