aed291…: “Outside of the happy town”

1 : Is the following radical a Type 1 or Type 2 Radical? $\sqrt {\sage {p1rad}}$

Yes! Since the radicand has more than one term (separated with a plus or minus sign) it is a type 2!

1.1 : Can you simplify this radical as it is currently written?

As mentioned in our lesson, the whole point of distinguishing the type 2 vs type 1, is that the radicand of a type 2 radical must be factored (or otherwise manipulated) before we have any hope of simplifying the radical!

2 : Is the following radical a Type 1 or Type 2 Radical? $\sqrt {\sage {p2rad}}$

Yes! Since this has everything inside looking like it has already been factored (i.e. each term is multiplying every other term) we have that this is a type 1 radical!

2.1 : Can you simplify this radical as it is currently written?

Since the original radical’s radicand is just one term (a.k.a. it appears “factored” already) we can potentially simplify the radical... there is hope! However, this also depends on the powers of the individual factors in the radicand, as well as the power of the radical. Thus it is potentially something that can be simplified further, but it may already be as simplified as it can get.

3 : Is the following radical a Type 1 or Type 2 Radical? $\sqrt {\sage {p3rad}}$

Yes! Since the radicand has more than one term (separated with a plus or minus sign) it is a type 2!

3.1 : Can you simplify this radical as it is currently written?

As mentioned in our lesson, the whole point of distinguishing the type 2 vs type 1, is that the radicand of a type 2 radical must be factored (or otherwise manipulated) before we have any hope of simplifying the radical!

4 : Is the following radical a Type 1 or Type 2 Radical? $\sqrt {\sage {p4rad}}$

Yes! Since this has everything inside looking like it has already been factored (i.e. each term is multiplying every other term) we have that this is a type 1 radical!

4.1 : Can you simplify this radical as it is currently written?

Since the original radical’s radicand is just one term (a.k.a. it appears “factored” already) we can potentially simplify the radical... there is hope! However, this also depends on the powers of the individual factors in the radicand, as well as the power of the radical. Thus it is potentially something that can be simplified further, but it may already be as simplified as it can get.

Press...	...to do
left/right arrows	Move cursor
shift+left/right arrows	Select region
ctrl+a	Select all
ctrl+x/c/v	Cut/copy/paste
ctrl+z/y	Undo/redo
ctrl+left/right	Add entry to list or column to matrix
shift+ctrl+left/right	Add copy of current entry/column to to list/matrix
ctrl+up/down	Add row to matrix
shift+ctrl+up/down	Add copy of current row to matrix
ctrl+backspace	Delete current entry in list or column in matrix
ctrl+shift+backspace	Delete current row in matrix

Type...	...to get
norm	$\|\|\blue{[?]}\|\|$
text	$\text{\blue{[?]}}$
sym_name	$\backslash\texttt{\blue{[?]}}$
abs	$\left\|\blue{[?]}\right\|$
sqrt	$\sqrt{\blue{[?]}}$
paren	$\left(\blue{[?]}\right)$
floor	$\lfloor \blue{[?]} \rfloor$
factorial	$\blue{[?]}!$
exp	${\blue{[?]}}^{\blue{[?]}}$
sub	${\blue{[?]}}_{\blue{[?]}}$
frac	$\dfrac{\blue{[?]}}{\blue{[?]}}$
int	$\displaystyle\int{\blue{[?]}}d\blue{[?]}$
defi	$\displaystyle\int_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}d\blue{[?]}$
deriv	$\displaystyle\frac{d}{d\blue{[?]}}\blue{[?]}$
sum	$\displaystyle\sum_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
prod	$\displaystyle\prod_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
root	$\sqrt[\blue{[?]}]{\blue{[?]}}$
vec	$\left\langle \blue{[?]} \right\rangle$
mat	$\left(\begin{matrix} \blue{[?]} \end{matrix}\right)$
*	$\cdot$
infinity	$\infty$
arcsin	$\arcsin\left(\blue{[?]}\right)$
arccos	$\arccos\left(\blue{[?]}\right)$
arctan	$\arctan\left(\blue{[?]}\right)$
sin	$\sin\left(\blue{[?]}\right)$
cos	$\cos\left(\blue{[?]}\right)$
tan	$\tan\left(\blue{[?]}\right)$
sec	$\sec\left(\blue{[?]}\right)$
csc	$\csc\left(\blue{[?]}\right)$
cot	$\cot\left(\blue{[?]}\right)$
log	$\log\left(\blue{[?]}\right)$
ln	$\ln\left(\blue{[?]}\right)$
alpha	$\alpha$
beta	$\beta$
gamma	$\gamma$
delta	$\delta$
epsilon	$\epsilon$
zeta	$\zeta$
eta	$\eta$
theta	$\theta$
iota	$\iota$
kappa	$\kappa$
lambda	$\lambda$
mu	$\mu$
nu	$\nu$
xi	$\xi$
omicron	$\omicron$
pi	$\pi$
rho	$\rho$
sigma	$\sigma$
tau	$\tau$
upsilon	$\upsilon$
phi	$\phi$
chi	$\chi$
psi	$\psi$
omega	$\omega$
Gamma	$\Gamma$
Delta	$\Delta$
Theta	$\Theta$
Lambda	$\Lambda$
Xi	$\Xi$
Pi	$\Pi$
Sigma	$\Sigma$
Phi	$\Phi$
Psi	$\Psi$
Omega	$\Omega$

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