MQ33 --- ℚ

Suppose ∛3 - √2 ∈ ℚ.
Let ∛3 - √2=q where q∈ ℚ.
∴∛3=q+√2
Rasing both sides to power 3:
3=q³+3√2q²+6q+2√2
⇒√2=(3-q³-6q)/(3q²+2)
⇒√2∈ ℚ.
Let √2=m/n where m, n∈ℤ and m, n are relatively prime.
∴m=√2n
squaring both sides:
m²=2n²⇒m is even
Let m=2k where k∈ℤ.
Then (2k)²=2n²⇒n²=2k²⇒n is even
∴m, n are both even. This contradicts that m, n are relatively prime.
∴∛3 - √2 ∉ ℚ.