Evaluating Nth Roots

Evaluating Nth Roots

Dr. Tom Giles

Open Ended

Based on your own understanding, what is a radical expression?

Open Ended

Based on your own understanding, what is a radical expression?

A radical expression is any mathematical expression containing a radical symbol.

Multiple Choice

$$\sqrt{45}$$  =

• $$3\sqrt{5}$$  

• $$5\sqrt{3}$$  

• $$9\sqrt{5}$$  

• $$5\sqrt{9}$$  

Multiple Choice

$$\sqrt{147}$$   Simplify

• $$3\sqrt{49}$$  

• $$6\sqrt{3}$$  

• $$7\sqrt{3}$$  

• $$9\sqrt{7}$$  

Multiple Choice

$$\sqrt{112}$$   Simplify

• $$4\sqrt{7}$$  

• $$16\sqrt{3}$$  

• $$16\sqrt{7}$$  

• $$4\sqrt{3}$$  

Multiple Choice

Examine the radical expression. What is the index?

• 5

• 108

• 36

Multiple Choice

Examine the radical expression. What is the radicand?

• 3

• 108

• 36

Multiple Choice

Examine the radical expression. Which question best represents this expression?

• What value can be multiplied by itself 108 times to obtain 5?

• What value can be multiplied by itself 5 times to obtain 108?

• What is the value of 108 divided by 5?

• What is the value of 5 divided by 108?

Multiple Choice

Write the given expression in exponential form.

• $$8^{\frac{10}{3}}$$
  

• $$10^{\frac{3}{8}}$$

• $$10^{\frac{8}{3}}$$
  

• $$3^{\frac{8}{10}}$$

Multiple Choice

Write the given expression in exponential form.

• $$h^{\frac{1}{2}}$$

• $$h^2$$

• $$h$$

• $$h^{\frac{1}{3}}$$

Multiple Choice

Write the given expression in radical form.

Multiple Choice

Write the given expression in radical form.

Multiple Choice

Which property of exponents could be used to prove the inverse property of radicals?

• Product of Powers

• Quotient of Powers

• Power of Power

Multiple Choice

Simplify the radical expression.

• $$18$$

• $$18^5$$

• $$\sqrt{18}$$

• $$3$$

Multiple Choice

Simplify the radical expression.

• $$6c$$

• $$6c^2$$

• $$36c^2$$

• $$\sqrt{6c}$$

Multiple Choice

Simplify the radical expression.

• $$d^3r$$  
  

• $$d^{12}r^4$$  
  

• $$\sqrt{d^3r}$$  
  

• $$\sqrt{d^{12}r^4}$$  
  

Multiple Choice

Which property of exponents could be used to prove the radical of product property of radicals?

• Power of Product

• Power of Quotient

• Power of Power

Multiple Choice

Rewrite (expand) the radical expression using the Radical of Product property.

Multiple Choice

Rewrite (condense) the radical expression using the Radical of Product property.

Multiple Choice

Which of the following is NOT a possible way to rewrite the given expression?

Multiple Choice

Which of the following is NOT a possible way to rewrite the given expression?

Multiple Choice

Which property of exponents could be used to prove the radical of quotient property of radicals?

• Power of Product

• Power of Quotient

• Power of Power

Multiple Choice

Which of the following is NOT a possible way to rewrite the radical expression?

Multiple Choice

Rewrite (expand) the radical expression using the Radical of Quotient property.

Multiple Choice

Rewrite (condense) the radical expression using the Radical of Quotient property.

Multiple Choice

Which property of exponents could be used to prove the radical of power property of radicals?

• Power of Product

• Power of Quotient

• Power of Power