These are five questions and five answers:
Question 1:
Answer: the third option.
Explanation:
1) simplify the first radical [tex]2ab[ \sqrt[3]{192ab^2}][/tex]
[tex]2ab[ \sqrt[3]{ 4^33ab^2}]=2ab(4) \sqrt[3]{3ab^2}=8ab \sqrt[3]{3ab^2} [/tex]
2) simplify the second radical
[tex]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} [/tex]
3) Subtract:
[tex]8ab \sqrt[3]{3ab^2} -15ab \sqrt[3]{3ab^2} [/tex]
[tex]8ab \sqrt[3]{3ab^2} -15ab \sqrt[3]{3ab^2} = -7ab \sqrt[3]{3ab^2} [/tex]
Question 2:
Answer: the third option
Explanation:
[tex]11 \sqrt{45}-4 \sqrt{5}=11 \sqrt{(9)(5)}-4 \sqrt{5} =11(3) \sqrt{5}-4 \sqrt{5}=33 \sqrt{5}-4 \sqrt{5} [/tex]
[tex]=29 \sqrt{5} [/tex]
Which is the third option
Question 3:
Answer: third option
Explanation:
[tex] \sqrt{8} +3 \sqrt{2} + \sqrt{32} =2 \sqrt{2} +3 \sqrt{2} +4 \sqrt{2} =9 \sqrt{2} [/tex]
Which is the third option
Question 4:
Answer: third option 14∛x
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
Explanation:
1) [tex]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} [/tex]
2) [tex]-2 \sqrt[4]{2y} -4 \sqrt[4]{32y}=-2 \sqrt[4]{2y} -4(2) \sqrt[4]{2y} =-10 \sqrt[4]{2y} [/tex]
3) Add (or subtract)
[tex]13 \sqrt[4]{x} -10 \sqrt[4]{2y} [/tex]
Which is the third option.
