Question
$(5+\sqrt{8})+(3-\sqrt{2})(\sqrt{2}-6)$ is:
✓
Answer
- Positive and irrational.
Solution:
$(5+\sqrt{8})+(3-\sqrt{2})(\sqrt{2}-6)$
$=(5+2\sqrt{2})+(3\sqrt{2}-18-2+6\sqrt{2})$
$=(5+2\sqrt{2})+(9\sqrt{2}-20)$
$=11\sqrt{2}-15$
And we know that the value of $11\sqrt{2}$ is greater than 15 so it's value will be positive,
And also sum or differences of rational and irrational is irrational.
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