6.1 Roots of Real Numbers/6.2 Properties of Radicals
6.3 Sums of Radicals
6.4 Binomials Containing Radicals
6.5 Equations Containing Radicals
6.6 Rational and Irrational Numbers/ 6.7 Imaginary Numbers /6.8 Complex Numbers
100
6.1
pg 262 #7
Simplify each expression. If the problem does not have a real number solution say so.
a.root()(7^2)
b. root(3)(7^3)
c. root(4)((-7)^4)
d. root(5)((-7)^5)
a.+-7
b.7
c.+-7
d.-7
100
6.3
pg272 #7
Simplify. If not possible say so
root()(6)+root()(36)+root()(216)
root()(6)+6+6root()(6)=6+7root()(6)
100
6.4
pg 275 #3
Simplify
(root()(7)+1)^2
(root()(7)+1)(root()(7)+1)=7+2root()(7)+1
100
6.5
pg.280 #7
Solve.
root(3)(3m+1)=4
3m+1=64
3m=63
m=21
100
6.6
pg286 #5
Classify each real number as either rational or irrational
a. 1.23
b. 1.\overline23
c. 1.2345678910111213...
a. Rat
b. Rat
c. Irra
200
6.1
pg. 262 #26
Find the real roots of the equation. If there are none, say so.
25y^2+16=17
y=+-1/5
200
6.3
pg273#43
Find the side x of the right triangle
10^2+root()(2)^2=x^2
100+2=x^2
+_root()(102)=x
200
6.3
pg276#37
What is the conjugate of
2root()(5)-3root()(2)
2root()(5)+3root()(2)
200
6.5
pg 280 #13
root()(x+2)=x
x+2=x^2
x^2-x-2=0
(x-2)(x+1)=0
x=2,-1
200
6.8
pg. 294
What is the complex conjugate of
-3/5-5i
-3/5+5i
300
6.2
pg.268 #10
Simplify.
root()(9/5)
3root()(5)/5
300
6.3
pg 272 #17
Simplify. If not possible say so
root(3)(4)+root(3)(1/2)
root(3)(4)+root(3)(1/2)*root(3)(4/4)
root(3)(4)+root(3)(4)/2
(3root(3)(4))/2
300
6.3
pg276 #39
Find x
(4+root()(2))^2+(4-root()(2))^2=x^2
16+8root()(2)+2+16-8root()(2)+2=x^2
36=x^2
x=+-6
300
6.5
pg 280 #25
Solve
root()(y)+root()(y+5)=5
root()(y+5)=5-root()(y)
y+5=25-10root()(y)+y
10root()(y)=20
root()(y)=2
y=4
300
6.6
pg 290 #18
Simplify
(-5i)^2
(-5i)(-5i)=25i^2=-25
400
6.2
pg. 268 #17
Simplify
root(3)(45)*root(3)(12)
root(3)(3^2*5)*root(3)(2^2*3)
3root(3)(20)
400
6.3
pg272 #27
(4root()(300)-root()(108))/root()(12)
(40root()(3)-6root()(3))/(2root()(3))=(34root()(3))/(2root()(3)
(34root()(3)*root()(3))/(2*3)=17
400
6.4
pg. 276#19
Simplify
(root()(15))/(root()(3)+root()(5))
(root()(15)*(root()(3)-root()(5)))/(3-5)
(root()(45)-root()(75))/-2
(3root()(5)-5root()(3))/-2
400
6.5
pg 280 #31
Solve
root()(x)+root()(3)=root()(x+3)
x+2xroot()(3)+3=x+3
2xroot()(3)=0
x=0
400
6.7
pg291#51
Simplify
root()(-x^5)+xroot()(-25x^2)-x^2root()(-25x)
ix^2root()(x)+5ix^2-5ix^2root()(x)
5ix^2-4ix^2root()(x)
500
6.2
pg. 268 #45
Simplify.
root(3)((27a)/(4b^4))
3root(3)(a/(2^2*b^4))
(3root(3)(2ab^2))/(2b^2)
500
6.3
pg 272 #41
root()(6w)*(root()(3w)+root()(2w^3))
root()(18w^2)+root()(12w^4)=3wroot()(2)+2w^2root()(3)
500
6.4
pg.276 #45
Simplify
(root()(a-root()(a))*root()(a+root()(a)))/root()(a-1)
(root()(a^2-a))/root()(a-1)=root()((a(a-1))/(a-1))=root()(a)
500
6.5
pg.280 #29
solve
root()(3b-2)-root()(2b+5)=1
root()(3b-2)=1+root()(2b+5)
3b-2=1+2root()(2b+5)+2b+5
b-8=2root()(2b+5)
b^2-16b+64=8b+20
b^2-16b+44=0
(b-22)(b-2)=0
b=22,2
500
6.8
pg296 #43
If
g(x)=(x-1)/(x+1)
Find
g(1+iroot()(3))
((1+iroot()(3))-1)/((1+iroot()(3))+1)=(iroot()(3))/(2+iroot()(3))
(iroot()(3)*(2-iroot()(3)))/(4+3)=(2iroot()(3)+3)/7