help with my pre calculus

Question

Divide and express each answer in simplest form. 

a. √(120) over √(10)

b. 8√(24) over 2√(3)

c. 6√(45x^5) over 8√(5x³)

Answer 1

a)

The radical expression is √(120)/√(10)

{Apply the radical property √(ab) = √a √b where a ≥ 0 and b ≥ 0}

= √(12*10)/√(10)

= [√(12)√(10)]/√(10)

= √(12)

= √(4*3)

= √4√3

= 2√3

√(120)/√(10) = 2√3.

Answer 2

b)

The radical expression is [8√(24)]/(2√3)

= [4√(24)]/√3

{Apply the radical property √(ab) = √a √b where a ≥ 0 and b ≥ 0}

= [4√(4*6)]/√3

= [4√4√6]/√3

= [4(2)√(3*2)]/√3

= [8√3√2)]/√3

= 8√2

[8√(24)]/(2√3) = 8√2.

Answer 3

c)

The radical expression is [6√(45x⁵)]/[8√(5x³)]

= [6√(9*5*x⁵)]/[8√(5x³)]

{Apply the radical property √(ab) = √a √b where a ≥ 0 and b ≥ 0}

= [6√9√(5x⁵)]/[8√(5x³)]

{Apply the exponent property a^m+n = (a^m)(aⁿ)}

= [6(3)√(5x³x²)]/[8√(5x³)]

= [18√(5x³)√(x²)]/[8√(5x³)]

= [18√(x²)]/8

= (18x)/8

= (9x)/4

[6√(45x⁵)]/[8√(5x³)] = (9x)/4.

Comments

is it 9x or 4?

 9x

____

  4

 

Thanks you so much!

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is it 9x over 4?

 9x

____

  4

 

Thanks you so much!

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yes, it is 9x over 4