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}}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B%5Csqrt%5B3%5D%7B144x%7D%7D%7B%5Csqrt%5B3%5D%7By%7D%7D~~%0A%5Cbegin%7Bcases%7D%0A144%3D2%5Ccdot%202%5Ccdot%202%5Ccdot%202%5Ccdot%203%5Ccdot%203%5C%5C%0A%5Cqquad%202%5E3%5Ccdot%2018%0A%5Cend%7Bcases%7D%5Cimplies%20%5Ccfrac%7B%5Csqrt%5B3%5D%7B2%5E3%5Ccdot%20%2018x%7D%7D%7B%5Csqrt%5B3%5D%7By%7D%7D%5Cimplies%20%5Ccfrac%7B2%5Csqrt%5B3%5D%7B%20%2018x%7D%7D%7B%5Csqrt%5B3%5D%7By%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B2%5Csqrt%5B3%5D%7B%20%2018x%7D%7D%7B%5Csqrt%5B3%5D%7By%7D%7D%5Ccdot%20%5Ccfrac%7B%5Csqrt%5B3%5D%7B%2818x%29%5E2%7D%7D%7B%5Csqrt%5B3%5D%7B%2818x%29%5E2%7D%7D%5Cimplies%20%5Ccfrac%7B2%5Csqrt%5B3%5D%7B%2818x%29%2818x%29%5E2%7D%7D%7B%5Csqrt%5B3%5D%7B%28y%29%2818x%29%5E2%7D%7D%5Cimplies%20%5Ccfrac%7B2%5Csqrt%5B3%5D%7B%2818x%29%5E3%7D%7D%7B%5Csqrt%5B3%5D%7B18%5E2x%5E2y%7D%7D)
![\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}}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B2%2818x%29%7D%7B%5Csqrt%5B3%5D%7B324x%5E2y%7D%7D~~%0A%5Cbegin%7Bcases%7D%0A324%3D2%5Ccdot%202%5Ccdot%203%5Ccdot%203%5Ccdot%203%5Ccdot%203%5C%5C%0A%5Cqquad%2012%5Ccdot%203%5E3%0A%5Cend%7Bcases%7D%5Cimplies%20%5Ccfrac%7B36x%7D%7B%5Csqrt%5B3%5D%7B12%5Ccdot%203%5E3x%5E2y%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B36x%7D%7B3%5Csqrt%5B3%5D%7B12x%5E2y%7D%7D%5Cimplies%20%5Ccfrac%7B12x%7D%7B%5Csqrt%5B3%5D%7B12x%5E2y%7D%7D)
Answer:
Step-by-step explanation:
3 times 4 is 12. you can solve this by dividing 12 by 3, or by skip counting and using repeated addition.
Answer: D
Step-by-step explanation: get the variable by itself on one side of the inequality sign.
Answer:
y = x/4 - 1/2
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Step 1: Write equation
x = 4y + 2
Step 2: Subtract 2 on both sides
x - 2 = 4y
Step 3: Divide both sides by 4
x/4 - 1/2 = y
The equation of a circle with center at (h,k) is
(x-h)^2+(y-k)^2=radius^2
given
(x-(-1))^2+(y-3)^2=9
center is (-1,3)
first option
