Operations with radicals

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

0/1
?
Intros
Lessons
  1. \cdotWhat is a "radical"?
    \cdotsquare root VS. cubic root
    \cdotcommon squares to memorize
0/16
?
Examples
Lessons
  1. Evaluating Radicals Algebraically
    Without using a calculator, evaluate:
    1. 9\sqrt { - 9}
    2. 327{^3}\sqrt{{ - 27}}
    3. 6164{^6}\sqrt{{\frac{1}{{64}}}}
    4. 481{^4}\sqrt{{ - 81}}
    5. 93649{^3}\sqrt{{64}}
  2. Evaluating Radicals Using a Calculator
    Use a calculator to determine:
    1.   6729{\;}{^6}\sqrt{{729}}
    2. 51024{^5}\sqrt{{-1024}}
    3. 532243{^5}\sqrt{{\frac{{32}}{{243}}}}
    4. 6600{^6}\sqrt{{600}}
    5. 50.5{^5}\sqrt{{0.5}}
    6. 34436\frac{3}{4}{^4}\sqrt{{36}}
  3. Radical Rules
    Combining radicals: Do's and Don'ts
    1. Determine whether the following statements are true or false.
      1. 2×3=6\sqrt 2 \times \sqrt 3 = \sqrt 6
      2. 2010=2\frac{{\sqrt {20} }}{{\sqrt {10} }} = \sqrt 2
      3. 15302=900\sqrt {15} \cdot\sqrt {30} \cdot\sqrt 2 = 900
      4. 35325=5{^3}\sqrt{5} \cdot {^3}\sqrt{{25}} = 5
    Topic Notes
    ?
    \cdot even root: evenpositive=defined{^{even}}\sqrt{positive}=defined
    i.e. 64=8\sqrt{64}=8
    evennegative=undefined{^{even}}\sqrt{negative}=undefined
    i.e. 64=undefined\sqrt{-64}=undefined

    \cdot odd root: oddpositive  or  negative=defined{^{odd}}\sqrt{positive\;or\;negative}=defined
    i.e. 364=4{^3}\sqrt{64}=4
    i.e. 364=4{^3}\sqrt{-64}=-4