Question #1 / 25
Simplify.
square root 18/50
Be sure to write your answer in lowest terms.
18
9
3
Answer: √50 = √25 = 5
Question #2 / 25
Rewrite the following in simplified radical form.
square root 20
√20 = √22 5 = 2√5
Question #3 / 25
Rewrite the following in simplified radical form.
square root 12y^8
Assume that all variables represent positive real numbers.
√12𝑦 8 = √322 (𝑦 4 )2 = 2y4√3
Question #4 / 25
Write the following expression in simplified radical form.
square root 75 t^9 w^10
Assume that all variables represent positive real numbers.
√75𝑡 9 𝑤 10 = √3(52 )(𝑡 4 )2 𝑡(𝑤 5 )2 = 5t4w5√3𝑡
Question #5 / 25
Simplify as much as possible.
3x^2 square root 96xw^2 + w square root 24x^5
Assume that all variables represent positive real numbers.
3x2√96𝑥𝑤 2 + 𝑤√24𝑥 5 = 12𝑥 2 𝑤√6𝑥 + 2𝑥 2 𝑤√6𝑥
= 14𝑥 2 𝑤√6𝑥
Question #6 / 25
Simplify.
square root 3v^2 u^2 square root 15v^2u^7
Assume that all variables represent positive real numbers.
√3𝑣 2 𝑢2 √15𝑣 2 𝑢7 =3v2u4√5𝑢
Answer: 3v2u4√5𝑢
Question #7 / 25
Multiply.
(6 square root 10 +4 square root 5) (square root 10-8 square root 5)
Simplify your answer as much as possible.
I did it in the post
Question #8 / 25
Rationalize the denominator and simplify.
square root 77/ square root 55
Answer:
√77
√55
=
√7
√5
=
√35
5
Question #9 / 25
Write in simplified radical form by rationalizing the denominator.
2 square root 3+4/ -2 square root 3+5
I did it in the file “3 Questions”
Question #10 / 25
Solve for ^v , where ^v is a real number. (it looks like the v is in the air or squared but it is
not in the equation?)
square root v-11=7
(If there is more than one solution, separate them with commas.)
Solution
√𝑣 − 11 = 7
v-11=72=49
v=49+11=60
Answer: v=60
Question #11 / 25
Solve for u, where u is a real number.
square root 7u-7 = square root 2u+2
(If there is more than one solution, separate them with commas.)
Solution:
√7𝑢 − 7 = √2𝑢 + 2
7u-7=2u+2
7u-2u=2+7
5u=9
u=9/5
Answer: u=9/5
Question #12 / 25
Solve for w, where w is a real number.
square root 5w+6=w
(If there is more than one solution, separate them with commas.)
Solution:
√5𝑤 + 6 = 𝑤
5w+6=w2
w2-5w-6=0
w=
5±√(−5)2 −4(1)(−6)
2
=(5 ± 7)/2= 6,-1
But only w=6 check the equation
Answer: w=6
Question #13 / 25
For the following right triangle, find the side x length . Round your answer to the nearest
tenth.
8 is on the short side and x is on the short side. The long side of the triangle or bottom is 12
Can you clarify the triangle ?
I did it in the file “3 Questions”
Question #14 / 25
Simplify. There isa a big 8 and it looks like the 2/3 is a square rrot
8 2/3
Solution:
82/3=(81/3 )2=22=4
Answer: 4
Question #15 / 25
Compute the following: 3 is on the outside and looks small
.
3 square root -27
Solution:
3
3
√−27 = √(−3)3 = −3
Answer: -3
Question #16 / 25
Write the following in simplified radical form. the 4 looks small and is on the outside
4 square root 96
4
4
4
√96 = √24 6 = 2√6
4
Answer: 2 √6
Question #17 / 25
Write the following expression in simplified radical form. the 5 looks small on the outside
5 square root 160x^11 y^5
Assume that all of the variables in the expression represent positive real numbers.
Solution
5
5
√160𝑥11 𝑦 5 = √25 5(𝑥 2 )5 𝑥𝑦 5
5
Answer: 2x2y√5𝑥
Question #18 / 25
Find the roots of the quadratic equation:
w^2-3w+2=0
(If there is more than one root, separate them with commas.)
Solution
w=
3±√32 −4(1)(2)
2
=(3±1)/2
Answer: 1,2
Question #19 / 25
Solve:
3u^2=u+4
(If there is more than one solution, separate them with commas.)
Solution
3u2-u-4=0
1±√1+48
u=
6
=
1±7
6
Answer: 4/3,-1
Question #20 / 25
Solve the equation
2y^2+4y+6=(y-1)^2
for y .
(If there is more than one solution, separate them with commas.)
Solution:
2y2+4y+6=y2-2y+1
y2+6y+5=0
y=
−6±√36−20
2
=
Answer: -1,-5
−6±4
2
Question #21 / 25
Solve x^2=27, where x is a real number.
Simplify your answer as much as possible.
If there is more than one solution, separate them with commas.
Solution:
x2=27 then: x=±√27 = ±3√3
Answer: -33, 33
Question #22 / 25
Solve (w-9)^2-72=0 , where w is a real number.
Simplify your answer as much as possible.
If there is more than one solution, separate them with commas.
Solution:
(w-9)2=72
w-9=±72=±62
w=9±62
Answer: 9-6√2, 9+6√2
Question #23 / 25
Compute the value of the discriminant and give the number of real solutions to the
quadratic equation.
7x^2-4x-1=0
Answer: discriminant is (-4)2-4(7)(-1)=16+28=44
2 real solutions
Question #24 / 25
Use the quadratic formula to solve for .
9x^2+x-2=0
(If there is more than one solution, separate them with commas.)
−1±√1+72
Solution: x=
Answer:
18
=
−1±√73
18
−1+√73 −1−√73
18
,
18
Question #25 / 25
When a ball is thrown, its height in feet h after t seconds is given by the equation
h=vt-16t^2,
where v is the initial upwards velocity in feet per second. If v=19 feet per second, find all
values of t for which h=5 feet. Do not round any intermediate steps. Round your answer to
2 decimal places.
(If there is more than one answer, enter additional answers with the button that says "or".)
Solution:
We have to find t where
5=19t-16t2
-16t2+19t-5=0
t=
−19±√41
−32
t = 0.3937, 0.7938
Answer: 0.39, 0.79