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Resources

Simplify radical expressions with variables II

\sqrt[4]{256 x^{32}}=

\square

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The root is not a real num

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Note that the radicand is nonnegative, so the fourth root is a real number.

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\sqrt[4]{81 x^{36}}

, find an expression such that, when it is raised to fourth p

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\left(3 x^{9}\right)^{4}=81 x^{36}

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\sqrt[4]{81 x^{36}}=3 x^{9}

Choose the correct symbol to compare the expressions. Do not multiply.

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9 \times \frac{2}{5}

9

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>

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<

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=

Choose the correct symbol to compare the expressions. Do not multiply.

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5 \times \frac{2}{3}

5

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>

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<

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=

Choose the correct symbol to compare the expressions. Do not multiply.

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9 \times \frac{1}{3}

9

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>

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<

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=

T

(in seconds) of a pendulum is given by

T=2\pi\sqrt{\left(\frac{L}{32}\right)}

L

stands for the length (in feet) of the pendulum

\pi=3.14

, and the period is

12.56

seconds, what is the length? The length of the pendulum is

\square

Select the expressions that are equivalent to

5m + 4m

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Multi-select Choices:

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m + 9m

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8m

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m \times 9

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m + 8m

The positive numbers

x

a-x

a

x

a

x \cdot(a-x)

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1

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\frac{a}{2}

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\sqrt{\frac{a}{2}}

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\sqrt{a}

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a

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(E) There is no

x

that would produce a maximum product

b

. Express your answer in simplest radical form if necessary.

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b=\sqrt{86} \cdot \sqrt{86}

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b=

c

. Express your answer in simplest radical form if necessary.

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c=-\sqrt{98} \cdot-\sqrt{98}

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c=

Solve the following equation for

x

. Express your answer in the simplest form.

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-(5 x-7)-3=5 x+2(-5 x+2)

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Simplify. Assume all variables are positive.

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\frac{w^{\frac{1}{3}}}{w^{\frac{4}{3}} \cdot w^{\frac{7}{3}}}

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Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

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Simplify. Assume all variables are positive.

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\frac{z^{\frac{1}{2}}}{z^{\frac{3}{2}} \cdot z^{\frac{3}{2}}}

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Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

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Simplify. Assume all variables are positive.

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\frac{s^{\frac{1}{2}}}{s^{\frac{3}{2}} \cdot s^{\frac{3}{2}}}

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Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

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Simplify. Assume all variables are positive.

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\frac{s^{\frac{4}{3}}}{s^{\frac{2}{3}} \cdot s^{\frac{1}{3}}}

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Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

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Simplify. Assume all variables are positive.

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\frac{c^{5/2}}{c^{5/2} \cdot c^{3/2}}

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Write your answer in the form

A

A/B

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

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Simplify. Assume all variables are positive.

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\frac{t^{\frac{3}{2}}}{t^{\frac{3}{2}} \cdot t^{\frac{1}{2}}}

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Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

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Simplify. Assume all variables are positive.

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\frac{b^{\frac{3}{2}}}{b^{\frac{3}{2}} \cdot b^{\frac{5}{2}}}

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Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

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Simplify. Assume all variables are positive.

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\frac{b^{\frac{4}{3}}}{b^{\frac{4}{3}} \cdot b^{\frac{1}{3}}}

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Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

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Evaluate the left hand side to find the value of

a

in the equation in simplest form.

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\frac{x^{\frac{4}{3}}}{x^{\frac{2}{3}}}=x^{a}

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\square

Simplify to a single trig function with no denominator.

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\csc ^{2} \theta \cdot \sin ^{2} \theta

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\sqrt{3}\sin x+3\cos x

A \sin(x+\alpha)

\sqrt{3}\sin x+3\cos x=\sqrt{3}

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0 \leq x \leq 2\pi

Which number, when placed in the box, will make the equation true?

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\square^{2}=\sqrt{64}

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\sqrt{8}

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\sqrt{32}

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16

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32

Use the given verices to calculate the coordinates of

\triangle L M N

after a dilation centered at the origin with scale factor

k=-3

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L(0,0), M(-4,1), N(-3,-6)

Follow the instructions below.

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a \cdot a^{2}

without exponents.

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a \cdot a^{2}=

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Fill in the blank.

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a \cdot a^{2}=a^{\square}

x

y

are both positive, write the following expression in simplest radical form.

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\sqrt{4x^{3}y^{7}}

Woo-Jin and Kiran were asked to find an explicit formula for the sequence

64, 16, 4, 1

, where the first term should be

f(1)

x

y

are both positive, write the following expression in simplest radical form.

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7 x \sqrt{9 x^{2} y^{4}}

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x

y

are both positive, write the following expression in simplest radical form.

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7 \sqrt{4 x^{5} y^{5}}

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x

y

are both positive, write the following expression in simplest radical form.

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x \sqrt{4 x^{6} y^{3}}

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y

-coordinate of the

y

-intercept of the polynomial function defined below.

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f(x)=x(x-5)\left(x^{2}-1\right)

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Answer the following True or False. Let

f(x)

be a increasing positive function. Then the right endpoint approximation is greater than the area under the curve.

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Simplify the radical expression.

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\sqrt{12x^{12}}

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Write your answer in the form

A

\sqrt{B}

A\sqrt{B}

A

B

are constants or expressions in

x

. Use at most one radical in your answer, and at most one absolute value symbol in your expression for

A

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