lesson 7-2 Advance

     To multiply radicals, consider the following, √(25) * √(9) = 5 * 3 = 15 and √(25) * √(9) = √(225) = 15, so √(25) * √(9) = √(25*9).

     as a general rule, √(a) * √(b) = √(ab)


     To simplify radicals, such as √(72), where there is no perfect square, you need to take the square out, so it would be √(2*6²), which would simplify as 6√2


     To divide radicals, consider the following, √(25)/√(9) = 5/3 and √(25)/√(9) = √(25/9) = √(5/3)² = 5/3


     as a general rule, if a and b are real numbers, and b does not equal zero, √(a)/√(b) = √(a/b)


      To rationalize the denominator, such as √(5)/√(3), make the bottom a perfect square, like this, √(5*3)/√(3*3). I multiplied both the top and bottom by √(3)/√(3) to make the denominator a perfect square, making the problem look like √(15)/3, which is rationalized.

*note, a number with an exponent of 1/2 is equal to taking the square root of it, an exponent of 1/3 is the same as the cube root.*

incase you don't quite understand

go to the next tab

incase next tab is closed, right click link and select open in new tab
http://phschool.com/webcodes10/index.cfm?wcprefix=age&wcsuffix=0702&area=view&x=5&y=9

Basic problems

1. √16 * √9
2. -5^1/3 * 25^1/3
3. √4 * √25
4. 8^1/3 * 27^1/3
5. √3 * √12
6. 3^1/3 * 9^1/3
7. √36 / √25
8. 32^1/3 / -4^1/3
9. (4² )^1/4
10. √2 / √3

Advanced problems

1.  √(72x³) 
2.  (80n⁵)^⅓ 
3.  (54x²y^³)⅓ * (5x³y⁴)⅓ 
4.  3√(7x³) * 2√(21x³y²) 
5. (1024x¹⁵)^1/4 / (4x)^1/4 
6.  (2/3x)⅓ 
7.  √((x³)/(5xy)) 
8.  3(5y³)⅓ * 2(50y⁴)⅓ 
9.  √(48x³)/√(3xy²)
10.  E=mc² , solve for c and rationalize the denominator
    
    
    Assume all variables are positive

scroll down

scroll down

scroll down

scroll down

answers

Beginner Level answers:

1. √16 * √9 = 4 * 3 = 12

2. ³√5 * ³√25 = ³√125 = 5

3. √4 * √25 = √100 = 10

4. ³√8 * ³√27 = 2*3 = 6

5. √3 * √12 = √36 = 6

6. ³√3 * ³√9 = ³√27 = 3

7. √36 / √25 = 6/5

8. ³√32 / ³√-4 = ³√64 / ³√-8 = -2

9. (4² )^{1/4 = 2}

10. √2 / √3 = √6 / 3

Advanced level answers

1. √(72x³) = √(6² * x²) * √(2 * x) = 6x√(2x)

2. ³√(80n⁵) = ³√(2³ * x³ * 10 * x²) = 2x ³√(10x²)

3. (54x²y^³)^⅓ * (5x³y⁴)^⅓ = 3y ³√(50x²y²) / 5xy²

4.  3√(7x³) * 2√(21x³y²) = 21x² √(3) / 42x²y

5. (1024x¹⁵)^1/4 / (4x)^{1/4 =} 4x^{4 4}√(x²) / x

6. (2/3x)⅓ = ³√(18x² ) / 3x

7. √((x³)/(5xy)) = x²√(5y) / 5xy

8. 3(5y³)⅓ * 2(50y⁴)⅓ = 6y ³√(1.5y²) / 10y²

9. √(48x³)/√(3xy²) = 4x/y

10. E = mc², c² = E/m, c = √(E/m), c = √(Em/m²), c = √(Em)/m

extra problems

will edit later