Review: Radicals and Rational Exponents

Review: Radicals and Rational Exponents

Simplify, Rewrite, Evaluate, Solve

Radicals

• Look for perfect square factors

• Break apart original into a product of two or more

• Find the square root of the perfect square!

Multiple Choice

Simplify √72

• 7√9
• 4√6
• 6√2
• 3√4

Multiple Choice

Simplify the following radical: √300

• 3√10
• 2√150
• 100√3
• 10√3

Multiple Choice

Reduce $\sqrt{3}\cdot\sqrt{3}$  to its simplest form.

•  $\sqrt{9}$  

•  $3\sqrt{1}$  

•  $3$  

•  $\left(\sqrt{3}\right)^2$  

Square root: the 1/2 power

• This property illustrates WHY the square root of x, squared, is just x

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Rational Exponents: Radical form

• Root number (type) is tiny number "on" the radical

• Any exponents inside the radical pertain to that particular radicand (base)

Rational Exponents: Exponential form

• From radical form, the root is the denominator, the "power" is the numerator

• Rewrite with the exponent as a fraction

Multiple Choice

In $a^{\frac{b}{c\ }}$  what does it transform to?

•  $\sqrt{a^c}$  

•  $\sqrt{a^{b\ }}$  

Multiple Choice

Rewrite in radical form.

 $\frac{\left(2x\right)^{\frac{1}{3}}}{\left(3y\right)^{\frac{3}{4}}}$  

•  $\frac{\ ^3\sqrt{2x}}{\ ^4\sqrt{\left(3y\right)^3}}$  

•  $\frac{\ ^3\sqrt{2x}}{\ ^3\sqrt{\left(3y\right)^4}}$  

•  $\frac{\ \sqrt{\left(2x\right)^3}}{\ ^4\sqrt{\left(3y\right)^3}}$  

•  $\frac{\ \sqrt{\left(2x\right)^3}}{\ ^3\sqrt{\left(3y\right)^4}}$  

Multiple Choice

Write in exponential form
∜(3x)³

• 3x³⁄ ⁴
• (3x)³∕ ⁴
• (3x)⁴⁄ ³
• 3x⁴⁄ ³

Multiple Choice

Rewrite the following

∛x⁵

• x^3/5

• x^5/3

• x²

• x³⋅x⁵

Fill in the Blank

Evaluate:

 $\sqrt{36^3}$  

Fill in the Blank

Evaluate:

 $16^{\frac{3}{4}}$  

Fill in the Blank

Evaluate:

Solving Radical Equations

• Isolate the Radical FIRST

• THEN, square both sides to remove radical(s)

Multiple Choice

• x = -6
• x = 3
• x = -3
• x = 5±

Multiple Choice

• 14
• -8
• 4
• -6

Rational Exponent Equations

• Isolate the radical/exponential term FIRST

• THEN, use reciprocal powers to solve

Multiple Choice

Solve for n.

• n=25

• n=-25

• n=5

• n=-5

Multiple Choice

Solve for p

• p=-7 and p=62/9

• p=7 and p=-62/9

• p=7

• p=-7

Multiple Choice

 $11\ =\ -5\ +4b^{\frac{2}{3}}$  

•  $\pm\ 8$  

•  $16$  

•  $8$  

•  $14.7$  

Multiple Choice

 $1024\ =\left(15n\ +\ 4\right)^{\frac{5}{3}}\$  

•  $4$  

•  $6935.2$  

•  $-48\ and\ \ 80$  

•  $\pm\ 4$  

Multiple Choice

Solve for m

• m=4

• m=32

• m=64

• m=-32