Question

HELP! Multiplying radicals. Questions on photo.

Answer 1

These are 10 questions and 10 answers

1)
`\sqrt[3]{24} . \sqrt[3]{45}`

Answer: third option 6∛5

Step-by-step 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)
`\sqrt[5]{4x^2} . \sqrt[5]{4x^2}`

Answer: second option.

Demostration:


`\sqrt[5]{4x^2} . \sqrt[5]{4x^2} = \sqrt[5]{4^2x^4} = \sqrt[5]{2^4x^4} = \sqrt[5]{16x^2}`

3)
`√(10) . √(10)`

Answer: first option 10

Justification:

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

4)
`\sqrt[4]{7} . \sqrt[4]{7} . \sqrt[4]{7} . \sqrt[4]{7}`

Answer: fourth option: 7

Step-by-step explanation:


`\sqrt[4]{7} . \sqrt[4]{7} . \sqrt[4]{7} . \sqrt[4]{7}= (\sqrt[4]{7^})^4= \sqrt[4]{7^4}=7 ^(4/4)=7^1=7`

5)
`(x √(7) -3 √(8)).(x √(7)-3 √(8))`

Answer: 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

Answer: the fourth option 6√6

Step-by-step explanation:

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

7)
`√(y^3) . √(y^3)`

Answer: first option y^3

Justification:


`√(y^3) . √(y^3) =( √(y^3) )^2 =(y^3)^(2/2)=y^3`

8) ∛d . ∛d . ∛d

Answer: first option: d

Step-by-step explanation:

∛d . ∛d . ∛d =
`( \sqrt[3]{d}) ^3 = d{3/3}=d^1=d`

9)
`√(5x^8y^2) . √(10x^3) . √(12y)`

Answer: second option

Step-by-step explanation:


`√(5x^8y^2) . √(10x^3) . √(12y) = √((5.10.12)x^8y^2x^3y)= \sqrt{600x^(11)y^3} =`


`=10x^5y √(6xy)`

10) (∛4) . √3

Answer: third option
`\sqrt[6]{432}`

Step-by-step explanation:


`\sqrt[3]{4} . √(3) = \sqrt[6]{4^2} . \sqrt[6]{3^3} = \sqrt[6]{16.27} = \sqrt[6]{432}`