Multiplying radicals. questions on photo.

These are 10 questions and 10 answers

1)

third option 6∛5

Explanation:

24 = 2^3 * 3

45 = 3^2 * 5

=> 24 * 45 = 2^3 * 3^3 * 5

=> (∛24).(∛45) = ∛[ (2^3).(3^3).5 ] = (2)(3)∛5 = 6∛5

2)

second option.

Demostration:

 

3)

first option 10

Justification:

√10 . √10 = (√10)^2 = √(10^2) = √100 = 10

4)

fourth option: 7

Explanation:



5)

the third option: 7x^2 - 12x√14 + 72

Solution:

Notice that it is the two factors are identical, so this is a perfect square binomial:

(x√7 - 3√8)^2 = (x√7)^2 - 2*(x√7)(3√8) + (3√8)^2 = 7x^2 - 6√(56)x + 72 =

= 7x^2 -(6)(2)x√14 + 72 = 7x^2 - 12x√14 + 72

6) √12 . √18

the fourth option 6√6

Explanation:

√12 . √18 = √ (2 . 2 . 3 . 2 . 3 . 3) = √ [( 2^3) . (3^3)] = 2 . 3 √6 = 6√6

7)

first option y^3

Justification:



8) ∛d . ∛d . ∛d

first option: d

Explanation:

∛d . ∛d . ∛d =    

9)

second option

Explanation:





10) (∛4) . √3

third option    

Explanation:

The density of the cube is 40