Properties of Radicals

Properties of Radicals

LT: I can simplify algebraic expression with radicals and rational exponents.

How do I simplify a radical?

Multiple Choice

Simplify $\sqrt{700}$ , if

 $\sqrt{700}=\sqrt{2\cdot2\cdot5\cdot5\cdot7}$  

•  $2\sqrt{35}$  

•  $7\sqrt{7}$  

•  $100\sqrt{7}$  

•  $10\sqrt{7}$  

•  $70\sqrt{10}$  

Multiple Choice

What is the prime factorization of 360?

• $36\cdot10$

• $2\cdot180$
  

• $2\cdot2\cdot5\cdot18$

• $2\cdot2\cdot2\cdot3\cdot3\cdot5$

• 360 is prime.

Multiple Choice

Simplify:

 $\sqrt{360}$  

•  $5\sqrt{5}$  
  

•  $5\sqrt{10}$  
  

•  $72\sqrt{5}$  

•  $6\sqrt{5}$  

•  $6\sqrt{10}$  

Multiple Choice

Simplify:

 $^3\sqrt{360}$  

•  $6\ \cdot\ ^3\sqrt{5}$  
  

•  $2\ \cdot\ ^3\sqrt{45}$  
  

•  $3\ \cdot\ ^3\sqrt{40}$  

•  $5\ \cdot\ ^3\sqrt{5}$  

• None of the above

Multiple Choice

Simplify:
 $\sqrt{8x^3}$  

•  $2\sqrt{x^3}$  

•  $2\sqrt{2x^3}$  

•  $2x\sqrt{2x}$  

•  $x\sqrt{8x}$  

•  $2x\sqrt{2}$  

What is a rational exponent?

Multiple Choice

Rewrite using radical form:

 $5^{\frac{1}{2}}$  

•  $\sqrt{5}$  

•  $\frac{5}{2}$  

•  $\left(\frac{1}{2}\right)^5$  

•  $5^2$  
  

•  $5\sqrt{2}$  

Multiple Choice

Rewrite using radical form:

 $13^{\frac{1}{3}}$  

•  $^3\sqrt{13}$  

•  $\frac{13}{3}$  

•  $\left(\frac{1}{3}\right)^{13}$  

•  $13^3$  

•  $13\sqrt{3}$  

Multiple Choice

Simplify:

 $36^{\frac{1}{2}}$  

•  $6$  

•  $1296$  

•  $18$  

•  $72$  

Multiple Choice

Simplify:

 $81^{\frac{1}{4}}$   

•  $9$  

•  $3$  

•  $21.25$  
  

•  $72$  

Multiple Select

Select all answers that are equivalent to:

 $4^{\frac{1}{2}}$  

•  $\sqrt{4}$  
  

•  $2$  
  

•  $4^2$  

•  $\sqrt{2^2}$  

How do I convert between radicals and rational exponents?

Conversion formula

•  $x^{\frac{m}{n}}=\ \ ^n\sqrt{x^m}$  

•  $x^{\frac{m}{n}}=\left(\ ^n\sqrt{x}\right)^m$  

Multiple Choice

Which expression is equivalent to:

 $\ ^5\sqrt{2^4}$  

•  $5^{\frac{2}{4}}$  

•  $2^{\frac{4}{5}}$  

•  $2^{\frac{5}{4}}$  

•  $4^{\frac{5}{2}}$  

•  $4^{\frac{2}{5}}$  

Multiple Choice

Which expression is equivalent to:

 $\ ^9\sqrt{x^7}$  

•  $9x^7$  
  

•  $x^{\frac{9}{7}}$  
  

•  $9^{\frac{7}{x}}$  

•  $9^{\frac{x}{7}}$  
  

•  $x^{\frac{7}{9}}$  
  

Multiple Select

Select all expressions that are equivalent to:

 $5^{\frac{3}{4}}$  

•  $\left(\ ^4\sqrt{5}\right)^3$  
  

•  $\left(\ ^4\sqrt{3}\right)^5$  
  

•  $\ ^4\sqrt{3^5}$  
  

•  $\ ^4\sqrt{5^3}$  
  

Multiple Select

Select all expressions that are equivalent to:

 $x^{\frac{5}{2}}$  

•  $\sqrt{x^5}$  

•  $\ ^5\sqrt{x^2}$  
  

•  $\left(\sqrt{x}\right)^5$  

•  $\left(^{\ 5}\sqrt{x}\right)^2$