Question

Please help!! Adding and subtracting radicals.

Answer 1

These are five questions and five answers:

Question 1:

Answer: the third option.

Step-by-step explanation:

1) simplify the first radical
`2ab[ \sqrt[3]{192ab^2}]`


`2ab[ \sqrt[3]{ 4^33ab^2}]=2ab(4) \sqrt[3]{3ab^2}=8ab \sqrt[3]{3ab^2}`

2) simplify the second radical



`5 \sqrt[3]{81a^4b^5} =5 \sqrt[3]{3^4a^4b^5} =5(3)ab \sqrt[3]{3ab^2} =15ab \sqrt[3]{3ab^2}`

3) Subtract:


`8ab \sqrt[3]{3ab^2} -15ab \sqrt[3]{3ab^2}`


`8ab \sqrt[3]{3ab^2} -15ab \sqrt[3]{3ab^2} = -7ab \sqrt[3]{3ab^2}`

Question 2:

Answer: the third option

Step-by-step explanation:


`11 √(45)-4 √(5)=11 √((9)(5))-4 √(5) =11(3) √(5)-4 √(5)=33 √(5)-4 √(5)`



`=29 √(5)`

Which is the third option

Question 3:

Answer: third option

Step-by-step explanation:


`√(8) +3 √(2) + √(32) =2 √(2) +3 √(2) +4 √(2) =9 √(2)`

Which is the third option

Question 4:

Answer: third option 14∛x

Step-by-step explanation:

This one just requires to add like terms:

5 (∛x) + 9(∛x) = (5 + 9) (∛x) = 14∛x , which is the third option.

Question 5.

Answer: third option

Step-by-step explanation:

1)
`2 \sqrt[4]{16x}+3 \sqrt[4]{81x}=2(2) \sqrt[4]{x} +3(3) \sqrt[4]{x} =4 \sqrt[4]{x} +9 \sqrt[4]{x} =13 \sqrt[4]{x}`

2)
`-2 \sqrt[4]{2y} -4 \sqrt[4]{32y}=-2 \sqrt[4]{2y} -4(2) \sqrt[4]{2y} =-10 \sqrt[4]{2y}`

3) Add (or subtract)


`13 \sqrt[4]{x} -10 \sqrt[4]{2y}`

Which is the third option.