Tag: ratio and proportions

The subtriplicate ratio of $a : b$ is $\sqrt [3]{a} : \sqrt [3]{b}$
$\therefore$ The subtriplicate ratio of $4913 : 2744$ is $\sqrt [3]{4913} : \sqrt [3]{2744} = 17 : 14$

The subtriplicate ratio of $a : b$ is $\sqrt [3]{a} : \sqrt [3]{b}$
$\therefore$ The subtriplicate ratio of $\sqrt {x} : \sqrt {y} = x^{\cfrac {1}{2}} : y^{\frac {1}{2}}$ is $(x^{\cfrac {1}{2}})^{\cfrac {1}{3}} : (y^{\cfrac {1}{2}})^{\cfrac {1}{3}}$
$= x^{\cfrac {1}{6}} : y^{\cfrac {1}{6}}$

The subtriplicate ratio of $a : b$ is $\sqrt [3]{a} : \sqrt [3]{b}$.
$\therefore$ The subtriplicate ratio of $64 : 729$ is $\sqrt [3]{64} = \sqrt [3]{729} = \sqrt [3]{(4)^{3}} : \sqrt [3]{(9)^{3}} = 4 : 9$.

The subtriplicate ratio of $a : b$ is $\sqrt [3]{a} : \sqrt [3]{b}$
Now, $3 : 81 = \dfrac {3}{81} = \dfrac {1}{27} = 1 : 27$
$\therefore$ The subtriplicate ratio of $1 : 27$ is $\sqrt [3]{1} : \sqrt [3]{27} = 1 : 3$

The reciprocal ratio of a:ba:b.

The subtriplicate ratio of $a : b$ is $\sqrt [3]{a} : \sqrt [3]{b}$.
$\therefore$ The subtriplicate ratio of $216 : 1331$ is $\sqrt [3]{216} : \sqrt [3]{1331} = \sqrt [3]{(6)^{3}} : \sqrt [3]{(11)^{3}}$
$= 6 : 11$

The subtriplicate ratio of $a : b$ is $\sqrt [3]{a} : \sqrt [3]{b}$
$\therefore$ The subtriplicate ratio of $2 : 3$ is $\sqrt [3]{2} : \sqrt [3]{3}$.

The reciprocal ratio of $a : b$ is $b : a$
$\therefore$ reciprocal ratio of $2 : 3$ is $3 : 2$

The reciprocal ratio of $a : b$ is $b : a$
$\therefore$ reciprocal ratio of $9x^{2} : 11x^{2}$ is $11x^{2} : 9x^{2}$

The reciprocal ratio of a:ba:b.