1 vote
489 views

### Simplify $\sqrt{8-\sqrt{63}}$ [duplicate]

I simplified the expression into $$\sqrt{8-3\cdot \sqrt{7}}$$ but my tutor said it wasn't the answer he was looking for. Can someone help me?
• 51
243 views

### Method for denesting square roots [duplicate]

Does anyone have a quick method of denesting square roots? Problem: To quickly denest $\sqrt{5+2 \sqrt{6}} \qquad \tag{1}$ As an aside, this comes from solving the polynomial $$x^4-10x^2+1=0$$ ...
158 views

### How to transform $\sqrt{5-2\sqrt{6}}$ to $\sqrt{3}-\sqrt{2}$ by arithmetic operations? [duplicate]

Three sides of a right-angled triangle are $2\sqrt{3}$ (hypotenuse), $\sqrt{6}+1$, & $\sqrt{5-2\sqrt{6}}$. How do I transform the third side's length to $\sqrt{3}-\sqrt{2}$ for making my life ...
• 3,186
152 views

### What is an algorithm to test whether a number field element has a square root in that number field? [duplicate]

Let $K$ be a number field, such as $\mathbb{Q}(\sqrt{d})$ for $d$ a square-free integer. I am looking for an algorithm that outputs whether some $\alpha \in K$ has a square root in $K$, i.e. when ...
• 3,999