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Math Problems
Grade 8
Relationship between squares and square roots
Simplify:
\newline
(
100
)
2
=
\sqrt{(100)^2} =
(
100
)
2
=
_____
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Simplify:
\newline
(
16
)
2
=
\sqrt{(16)^2} =
(
16
)
2
=
___
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Simplify:
\newline
(
25
)
2
=
\sqrt{(25)^2} =
(
25
)
2
=
_____
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Simplify:
\newline
(
36
)
2
=
(\sqrt{36})^2 =
(
36
)
2
=
_____
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Simplify:
\newline
(
49
)
2
=
(\sqrt{49})^2 =
(
49
)
2
=
_____
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Simplify:
\newline
(
9
)
2
=
(\sqrt{9})^2 =
(
9
)
2
=
_____
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Simplify:
\newline
(
4
)
2
=
\sqrt{(4)^2} =
(
4
)
2
=
_____
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Simplify:
\newline
(
4
)
2
=
(\sqrt{4})^2 =
(
4
)
2
=
_____
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Simplify:
\newline
(
81
)
2
=
(\sqrt{81})^2 =
(
81
)
2
=
_____
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Find square root of
1225
1225
1225
using prime factorisation.
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Find the smallest number by which
3645
3645
3645
must be divided so that it becomes a perfect square. Also, find the square root of the resulting number.
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Compute:
\newline
93000
÷
1
0
3
93000 \div 10^{3}
93000
÷
1
0
3
\newline
Answer:
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What is the value of
ln
e
2
3
\ln \sqrt[3]{e^{2}}
ln
3
e
2
?
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Fully simplify.
\newline
(
3
x
2
+
y
3
)
2
\left(3 x^{2}+y^{3}\right)^{2}
(
3
x
2
+
y
3
)
2
\newline
Answer:
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Simplify:
\newline
(
−
6
x
2
)
3
\left(-6 x^{2}\right)^{3}
(
−
6
x
2
)
3
\newline
Answer:
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Simplify:
\newline
(
9
x
4
)
2
\left(9 x^{4}\right)^{2}
(
9
x
4
)
2
\newline
Answer:
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Solve for
x
\mathrm{x}
x
:
\newline
2
x
+
26
−
10
=
−
4
\sqrt{2 x+26}-10=-4
2
x
+
26
−
10
=
−
4
\newline
Answer:
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Fully simplify.
\newline
(
4
x
y
)
2
(4 x y)^{2}
(
4
x
y
)
2
\newline
Answer:
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Fully simplify.
\newline
(
3
x
y
3
)
2
\left(3 x y^{3}\right)^{2}
(
3
x
y
3
)
2
\newline
Answer:
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Simplify to a single power of
4
4
4
:
\newline
4
3
×
4
4^{3} \times 4
4
3
×
4
\newline
Answer:
4
□
4 ^\square
4
□
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Simplify to a single power of
4
4
4
:
\newline
4
4
×
4
4^{4} \times 4
4
4
×
4
\newline
Answer:
4
□
4 ^\square
4
□
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Write the number
4.4
×
1
0
2
4.4 \times 10^{2}
4.4
×
1
0
2
in standard form.
\newline
Answer:
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lim
x
→
−
1
5
−
11
x
=
\lim _{x \rightarrow-1} \sqrt{5-11 x}=
lim
x
→
−
1
5
−
11
x
=
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lim
x
→
−
∞
16
x
4
−
8
x
2
x
2
−
2
=
\lim _{x \rightarrow-\infty} \frac{\sqrt{16 x^{4}-8 x^{2}}}{x^{2}-2}=
lim
x
→
−
∞
x
2
−
2
16
x
4
−
8
x
2
=
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lim
x
→
−
∞
6
x
2
−
x
9
x
4
+
7
x
3
=
\lim _{x \rightarrow-\infty} \frac{6 x^{2}-x}{\sqrt{9 x^{4}+7 x^{3}}}=
lim
x
→
−
∞
9
x
4
+
7
x
3
6
x
2
−
x
=
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log
8
64
=
\log _{8} 64=
lo
g
8
64
=
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log
8
1
=
\log _{8} 1=
lo
g
8
1
=
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log
16
4
=
\log _{16} 4=
lo
g
16
4
=
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log
27
9
=
\log _{27} 9=
lo
g
27
9
=
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log
8
2
=
\log _{8} 2=
lo
g
8
2
=
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log
4
8
=
\log _{4} 8=
lo
g
4
8
=
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log
12
1
=
\log _{12} 1=
lo
g
12
1
=
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log
3
1
=
\log _{3} 1=
lo
g
3
1
=
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log
2
32
=
\log _{2} 32=
lo
g
2
32
=
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log
125
5
=
\log _{125} 5=
lo
g
125
5
=
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log
9
3
=
\log _{9} 3=
lo
g
9
3
=
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log
16
8
=
\log _{16} 8=
lo
g
16
8
=
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log
5
25
=
\log _{5} 25=
lo
g
5
25
=
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log
49
7
=
\log _{49} 7=
lo
g
49
7
=
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log
3
27
=
\log _{3} 27=
lo
g
3
27
=
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log
7
49
=
\log _{7} 49=
lo
g
7
49
=
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log
4
16
=
\log _{4} 16=
lo
g
4
16
=
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log
1
2
32
=
\log _{\frac{1}{2}} 32=
lo
g
2
1
32
=
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log
10
1
=
\log _{10} 1=
lo
g
10
1
=
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log
2
8
=
\log _{2} 8=
lo
g
2
8
=
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log
5
125
=
\log _{5} 125=
lo
g
5
125
=
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Solve the following equation for
y
y
y
.
\newline
y
+
6
=
2
y
2
+
72
y
=
□
\begin{array}{l} y+6=\sqrt{2 y^{2}+72} \\ y=\square \end{array}
y
+
6
=
2
y
2
+
72
y
=
□
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9
100
\sqrt{9^{100}}
9
100
\newline
Which of the following values is equivalent to the given expression?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
10
3^{10}
3
10
\newline
(B)
9
10
9^{10}
9
10
\newline
(C)
3
100
3^{100}
3
100
\newline
(D)
9
98
9^{98}
9
98
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The quotient of
m
4
5
m
3
4
\frac{\sqrt[5]{m^{4}}}{\sqrt[4]{m^{3}}}
4
m
3
5
m
4
and
m
m
6
5
\frac{\sqrt{m}}{\sqrt[5]{m^{6}}}
5
m
6
m
is equal to
m
y
m^{y}
m
y
. What is the value of
y
y
y
?
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What is the value of
cos
(
6
0
∘
)
?
\cos \left(60^{\circ}\right) ?
cos
(
6
0
∘
)
?
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