ProphetesAI is thinking...
surd
MindMap
Loading...
Sources
surd
▪ I. surd, a. and n. (sɜːd) Also 6–7 surde. [ad. L. surdus (in active sense) deaf, (in pass. sense) silent, mute, dumb, (of sound, etc.) dull, indistinct. The mathematical sense ‘irrational’ arises from L. surdus being used to render Gr. ἄλογος (Euclid bk. x. Def.), app. through the medium of Arab. ...
Oxford English Dictionary
prophetes.ai
Surd, Hungary
Surd ( ) is a village in Zala County, Hungary.
The village is best known for its production of Christmas trees. Culture
The Hungarian folk song Röpülj, páva, röpülj was collected in 1935 in Surd by Vilmos Seemayer.
wikipedia.org
en.wikipedia.org
surd
surd/sɜ:d; səd/ n (mathematics 数) mathematical quantity, esp a root, that cannot be expressed as an ordinary number or quantity 不尽根 The square root of 5 (5) is a surd. 5 的平方根（5）是不尽根.
牛津英汉双解词典
prophetes.ai
Simplify the surd expression. Simplify the surd. $(2\sqrt 3 + 3\sqrt 2)^2$ I know I should us this formula: $(a^2+2ab+b^2)$ But this gets complicated later. Please explain. :(
Applying the formula you get $$(2\sqrt3+3\sqrt2)^2 = 4\cdot3 + 2\cdot 2\sqrt3\cdot 3\sqrt 2 + 9\cdot 2 = 30 + 12\sqrt6$$
prophetes.ai
$\surd (I^e)=(\surd I)^e$ I'm trying to solve this question: =(\surd I)^e$ in the part (ii). I'm trying a lot proving the inclusions $\subset$ and $\supset$ without ...
Let $r \in \sqrt{I}$. That means $r^n \in I$ for some $n > 0$. But then $$f(r)^n = f(r^n) \in f(I) = I^e,$$ so $f(r) \in \sqrt{I^e}$, thus $f(\sqrt{I}) = (\sqrt{I})^e \subset \sqrt{I^e}$. Conversely, let $s \in \sqrt{I^e}$ and $r \in f^{-1}(\\{s\\})$ (since $f$ is surjective, such an $r$ exists). Le...
prophetes.ai
Rationalize the denominator of the surd, giving your answer in the simplest form. Rationalize the denominator of the surd, giving your answer in the simplest form. $\frac {3}{\sqrt2+5} $ Please help me... It must b...
Yes, you've got a great start. Now, simply multiply the numerators and the denominators, $$\frac {3}{\sqrt2+5} * \frac{\sqrt2-5}{\sqrt2-5} = \dfrac{3(\sqrt 2 -5)}{(\sqrt 2 + 5)(\sqrt 2 - 5)}$$ - and in the denominator, use the fact that $$(a +b)(a-b) = a^2 - b^2$$
prophetes.ai
Surd inside Surd equality I was trying a problem where I got the following surd as my answer: $$ {\sqrt{6 - 2 \sqrt{5} }\over 4} \approx 0.309016.... $$ The answer listed was: $$ {\sqrt{5} - 1 \over 4} \approx 0.30...
Suppose you assume that you can write $\sqrt{6-2\sqrt5} = \sqrt a - \sqrt b$ for some rational numbers $a$ and $b$. Squaring both sides will give you $6-2\sqrt5 = a+b-2\sqrt{ab}$, and so \begin{align*} 6 &= a+b \\\ \sqrt{5} &= \sqrt{ab} \end{align*} So we want $ab=5$ and $a+b=6$. An obvious solution...
prophetes.ai
Divisibility of ceiling function of surd Show that: The integer next greater than $(\sqrt{7}+\sqrt{3})^{2n}$ is divisible by $4^n$
Hint: Show that $$ (\sqrt7+\sqrt3)^{2n}+(\sqrt7-\sqrt3)^{2n} $$ is an integer. Also $\sqrt7-\sqrt3<1$.
prophetes.ai
Simplifying a dividing surd? Can anyone explain how I would simplify this dividing surd: $$\frac{3\sqrt{14}}{\sqrt{42}}$$ As far as I can see $\sqrt{14}$ and $\sqrt{42}$ can't be simplified, right? So how does the d...
$$\frac{3\sqrt{14}}{\sqrt{42}}=\frac{3\sqrt{14}}{\sqrt{3}\sqrt{14}}=\frac{3}{\sqrt{3}}=\sqrt{3}$$
prophetes.ai
Trigonometry question: Find in simplest surd form: $\cos 195^{\circ}$ Find in simplest surd form: $\cos 195^{\circ}$. Ive recently been doing the trigonometry topic form textbook and have oftenly come across these qu...
Assume that we are working with angles in degrees. Hint: $$\cos(195) = \cos(180 + 15)$$ Another hint: > Now split $\cos(180 + 15)$ using $\cos(A+B) = \cos(A)\cos(B)-\sin(A)\sin(B)$. And another: > Substitute $\sin(180) = 0$ and $\cos(180) = -1$. Nearly done: > Notice that $\cos(15) = \cos(30/2)$ and...
prophetes.ai
A Very Short Question On Surd Notation{Square Root} What makes $\sqrt[7]{9}$ = $9^\frac{1}{7}$ Can this be explained using laws of indices?
Well, do you agree that $\sqrt[7]9$ is a number such that $(\sqrt[7]9)^7=9$? Now, suppose $$\begin{align*}\sqrt[7]9&=9^x\\\ (\sqrt[7]9)^7&=(9^x)^7 \tag 1\\\ 9^{7x}&=9 \tag 2\\\7x&=1 \tag 3\\\ x&=\dfrac 1 7\end{align*}$$ We have used in going from $(1)$ to $(2)$ that, $$(x^a)^b=x^{ab}$$ In going from...
prophetes.ai
Rationalize a surd $\frac{1}{1+\sqrt{2}-\sqrt{3}}$ How can I rationalize the following surd $$\frac{1}{1+\sqrt{2}-\sqrt{3}}$$ What would be the conjugate of the denominator
Rationalise twice, because after rationalising once , there would still remain a surd in the denominator.
prophetes.ai
solving a quadratic in surd form I am trying to come up with a surd solution for this quadratic: $$-2s^2-s+3=0$$ I can only seem to find a roots in decimal form, namely $x = \frac{-2}{3}$ or $x = 1$ The question spe...
$f(s) = -2s^2-s+3 =0\implies s^2+\frac{s}{2}-\frac{3}{2}=0$ Then $$(s+\frac{1}{4})^2-\frac{3}{2}-\frac{1}{16}=0$$ $$(s+\frac{1}{4})^2=\frac{1+24}{16}=\frac{25}{16}$$ $$s=\frac{-1\pm 5}{4}\implies s= -\frac{3}{2} \quad\text{or}\quad s=1$$ If you insist on writing them inside a square root, then: $s= ...
prophetes.ai
Evaluate if $\sin10°$ be expressed in real surd form? > **Possible Duplicate:** > Calculating $\sin(10^\circ)$ with a geometric method Evaluate if $\sin10°$ be expressed in real surd form? Thank you!
Let $x$ be the sine of the $10$ degree angle. Note the identity $$\sin(3x)=3\sin x-4\sin^3 x.$$ This identity can be proved by using the addition laws for sine and cosin repeatedly, starting with $\sin(3x)=\sin(2x+x)=\sin 2x \cos x +\cos 2x\sin x$. The sine of the $30$ degree angle is $1/2$, Thus we...
prophetes.ai
Representing $\frac{3 + \sqrt{5}}{2}$ as a square of a quadratic surd How can I represent $\frac{3 + \sqrt{5}}{2}$ as square of a quadratic surd? Actually, I was solving a question where $\frac{3 + \sqrt{5}}{2}$ was c...
We can set $(a+b\sqrt{5})^2=\frac{3}{2} + \frac{1}{2}\sqrt{5}$. Then, solve for rational $a$ and $b$. Comparing the terms we obtain: $$a^2 + 5b^2 = \frac{3}{2},\ \ \ 2ab = \frac{1}{2}$$ Solving for $a$ and $b$, we get $a=b=\frac{1}{2}$ or $a=b=-\frac{1}{2}$, thus the two possible squares are: $$ \le...
prophetes.ai