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OpenStudy (anonymous):

algebra II, 7 questions, please help? I've tried everything and I still don't know these

OpenStudy (anonymous):

I will fan and give medal

OpenStudy (anonymous):

i will try if i can help

OpenStudy (anonymous):

give me one or some of them

OpenStudy (anonymous):

OpenStudy (anonymous):

question 2: rationalize the denomenator

OpenStudy (anonymous):

4.66001381463

OpenStudy (anonymous):

thats not one of my choices

OpenStudy (anonymous):

show me your choices

OpenStudy (anonymous):

16.8209311619

OpenStudy (anonymous):

is that one of your choices?

OpenStudy (anonymous):

or 9.7

OpenStudy (anonymous):

im pretty sure its 9.7

OpenStudy (anonymous):

MY CHOICES ARE:

OpenStudy (anonymous):

Rationalize the denominator by multiplying by its conjugate:\[\frac3{6-\sqrt5}\times\frac{6+\sqrt5}{6+\sqrt5}=\frac{18+3\sqrt5}{31}\]

OpenStudy (anonymous):

There is seven questions, the first one im trying to do is

OpenStudy (anonymous):

Distribute:\[\sqrt5(10-4\sqrt2)=10\sqrt5-4\sqrt10\]

OpenStudy (anonymous):

multiply by 6+sqrt(x)

OpenStudy (anonymous):

identify the conjugate of

OpenStudy (anonymous):

4-sqrt(7) i think

OpenStudy (anonymous):

OpenStudy (anonymous):

The conjugate of an expression with a square root like \(a+b\sqrt{c}\) is always given by \(a-b\sqrt{c}\). The point of this whole concept is that it aids in simplifying expressions, since multiplying the expression by its conjugate yields a difference of squares free of radicals: \((a+b\sqrt{c})(a-b\sqrt{c})=a^2-ab\sqrt{c}+ab\sqrt{c}-b^2\sqrt{c}^2=a^2-b^2c\)!

OpenStudy (anonymous):

distribute

OpenStudy (anonymous):

would the answer be this?

OpenStudy (anonymous):

Distribute: \[\begin{align*}(4-\sqrt3)(12+5\sqrt3)&=4(12+5\sqrt3)-\sqrt3(12+5\sqrt3)\\&=48+20\sqrt3-12\sqrt3-5\sqrt3^2\\&=48+8\sqrt3-15\\&=33+8\sqrt3\end{align*}\]

OpenStudy (anonymous):

rationalize the denominator

OpenStudy (anonymous):

Multiply both the numerator and denominator by \(\sqrt2\) to get rid of your radical.\[\frac3{\sqrt2}\times\frac{\sqrt2}{\sqrt2}=\frac{3\sqrt2}{\sqrt2^2}=\frac{3\sqrt2}2\]

OpenStudy (anonymous):

you should know better than to post a whole assignment here without even trying it first !!

OpenStudy (anonymous):

\[\sqrt{10}x \sqrt{8}\]

OpenStudy (anonymous):

the x is multiply

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