1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Kruka [31]
3 years ago
11

Rationalize the numerator.

rt%5B3%5D%7By%7D%20%7D%20" id="TexFormula1" title=" \frac{ \sqrt[3]{144x } }{ \sqrt[3]{y} } " alt=" \frac{ \sqrt[3]{144x } }{ \sqrt[3]{y} } " align="absmiddle" class="latex-formula">
Mathematics
2 answers:
Simora [160]3 years ago
3 0

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}}

Kipish [7]3 years ago
3 0

 ∛144x

-----------

   ∛y


   ∛8 ∛18x           ∛y^2

= -------------- * ----------------

    ∛y                    ∛y^2


    2 ∛18xy^2

= ------------------

          ∛y^3


     2 ∛18xy^2

= ------------------

           y

You might be interested in
4p + 1 = 10 what is the value of p?
fredd [130]

Answer:

p = 9/4 or 2.25

Step-by-step explanation:

4p + 1 = 10

      -1     -1

4p = 9

Divide 4 on both sides

p = 9/4 or 2.25

5 0
3 years ago
Read 2 more answers
Y=5x-4
anyanavicka [17]

Answer:

\displaystyle -5x + y = -92\:or\:y = 5x - 92

Step-by-step explanation:

−12 = 5[16] + b

80

\displaystyle -92 = b \\ \\ y = 5x - 92

If you want it in <em>Standard</em><em> </em><em>Form</em>:

y = 5x - 92

- 5x - 5x

__________

\displaystyle -5x + y = -92

I am joyous to assist you anytime.

7 0
3 years ago
A bus travels two different routes: the Green Route and the Blue Route.
Alex17521 [72]

Answer:4.5

Step-by-step explanation: Check the file for my explanation

8 0
2 years ago
Which symbol makes the statement true? 125.32 ____ 125.093<br><br> &lt;<br> &gt;<br> =<br> ≥
Alexandra [31]
Hello : 
125.32  > 125.093 .. because : 3 <span>> 0</span>
4 0
3 years ago
Read 2 more answers
Translate this phrase into an algebraic expression.
Verizon [17]

Answer:

Step-by-step explanation:

9n-2

5 0
2 years ago
Other questions:
  • Which person has the highest hourly wage? Kevin? Savannah? Greg?
    9·1 answer
  • Find 3 consecutive even integers if their sum decreased by 10 equals -22
    7·1 answer
  • Value of x is 3.2x-9.6=38.4?
    6·1 answer
  • Multiply. Write in simplest form.<br><br> 1. 5 1/3x1 1/4<br> 2.1 2/5x3 1/6<br> 3.7 1/8x2 5/6
    6·2 answers
  • Lisa’s cameras has 2,048 megabytes of memory for storing pictures. She already used half this amount. A high-quality pictures us
    8·1 answer
  • Helpppp plzzzzzzzzzzzzzzz
    5·1 answer
  • Solve for − ∣ x − 2 ∣ + 4 ≤ 0
    7·1 answer
  • PLEASE HELP ME ASAP??!!<br> Classify the following triangle. Check all that apply.
    5·1 answer
  • I need help with this question <br><br>Help needed!!!!!!
    8·1 answer
  • Alex eats 2 pieces of candy. Marisol eats 3 times as many pieces of candy as Alex. Which equation can be used to determine the a
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!