Question

Show that

Answer 1

Answer:

• See below

Step-by-step explanation:

Use same power to compare the values

Prove the first part:

• $\sqrt[3]{3}+\sqrt{2} >\sqrt[3]{9}$
• $\sqrt[6]{3^2}+\sqrt[6]{2^3} >\sqrt[6]{9^2}$
• $\sqrt[6]{9}+\sqrt[6]{8} >\sqrt[6]{81}$
• $\sqrt[6]{9}+\sqrt[6]{8}> \sqrt[6]{8}+\sqrt[6]{8}=2\sqrt[6]{8}=\sqrt[6]{8*64} =\sqrt[6]{512} >\sqrt[6]{81}$
• $512 > 81$

Prove the second part:

• $\sqrt[3]{9} >\sqrt[4]{13}$
• $\sqrt[12]{9^4} >\sqrt[12]{13^3}$
• $\sqrt[12]{6561} >\sqrt[12]{2197}$
• $6561 > 2197$