75/6.98=10.744
We would most likely round this down to 10 even though the .7 because if we round up we would go over the budget.
So he can buy about 10 CDs

7 0

3 years ago

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Rationalize the numerator. <img src="https://tex.z-dn.net/?f=%20%20%5Cfrac%7B%20%5Csqrt%5B3%5D%7B144x%20%7D%20%7D%7B%20%5Csq

Simora [160]

rationalizing the numerator, or namely, "getting rid of that pesky radical at the top".

we simply multiply top and bottom by a value that will take out the radicand in the numerator.

$\bf \cfrac{\sqrt[3]{144x}}{\sqrt[3]{y}}~~
\begin{cases}
144=2\cdot 2\cdot 2\cdot 2\cdot 3\cdot 3\\
\qquad 2^3\cdot 18
\end{cases}\implies \cfrac{\sqrt[3]{2^3\cdot 18x}}{\sqrt[3]{y}}\implies \cfrac{2\sqrt[3]{ 18x}}{\sqrt[3]{y}}
\\\\\\
\cfrac{2\sqrt[3]{ 18x}}{\sqrt[3]{y}}\cdot \cfrac{\sqrt[3]{(18x)^2}}{\sqrt[3]{(18x)^2}}\implies \cfrac{2\sqrt[3]{(18x)(18x)^2}}{\sqrt[3]{(y)(18x)^2}}\implies \cfrac{2\sqrt[3]{(18x)^3}}{\sqrt[3]{18^2x^2y}}$

$\bf \cfrac{2(18x)}{\sqrt[3]{324x^2y}}~~
\begin{cases}
324=2\cdot 2\cdot 3\cdot 3\cdot 3\cdot 3\\
\qquad 12\cdot 3^3
\end{cases}\implies \cfrac{36x}{\sqrt[3]{12\cdot 3^3x^2y}}
\\\\\\
\cfrac{36x}{3\sqrt[3]{12x^2y}}\implies \cfrac{12x}{\sqrt[3]{12x^2y}}$