query: Showing that $[\mathbb{Q}(\sqrt{m_1},\sqrt{m_2},\ldots, \sqrt{m_t}):\mathbb{Q}]=2^t$
positive_passages.docid: 27784
positive_passages.text: Proving that $\left(\mathbb Q[\sqrt p_1,\dots,\sqrt p_n]:\mathbb Q\right)=2^n$ for distinct primes $p_i$.
negative_passages.docid: 129521
negative_passages.text: Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
negative_passages.docid: 4228
negative_passages.text: Prove that the only automorphism of $\mathbb{Q}(\sqrt[3]{2})$ is the identity automorphism.
negative_passages.docid: 38549
negative_passages.text: $\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$
negative_passages.docid: 61103
negative_passages.text: Prove that $\mathbb{|Q| = |Q\times Q|}$
negative_passages.docid: 95111
negative_passages.text: Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.
negative_passages.docid: 72144
negative_passages.text: Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
negative_passages.docid: 51706
negative_passages.text: If $(k,l) = 1$, show that $(b_2k-b_1l, a_1l-a_2k) = 1$ for $a_1b_2-a_2b_1=1$
negative_passages.docid: 76188
negative_passages.text: Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
negative_passages.docid: 34693
negative_passages.text: Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
negative_passages.docid: 99835
negative_passages.text: Polynomial in $\mathbb{Q}[x]$ with root $\sqrt[3]{2}+\sqrt[3]{3}$
negative_passages.docid: 62485
negative_passages.text: How can I prove $\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}...}}}}=2$
negative_passages.docid: 103854
negative_passages.text: Showing that $Q_n=D_n+D_{n-1}$
negative_passages.docid: 101057
negative_passages.text: Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$
negative_passages.docid: 3109
negative_passages.text: Prove that $(p+q)^m \leq p^m+q^m$
negative_passages.docid: 35342
negative_passages.text: Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$
negative_passages.docid: 58009
negative_passages.text: How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$