Tag: composition of ratios

The subduplicate ratio of $x^{4} : y^{2}$ is $\sqrt {x^{4}} : \sqrt {y^{2}} = x^{2} : y$

The subtriplicate ratio of $a : b$ is $\sqrt [3]{a} : \sqrt [3]{b}$
$\therefore$ The subtriplicate ratio of $27 : 125$ is $\sqrt [3]{27} : \sqrt [3]{125} = 3 : 5$.

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

The reciprocal ratio of $a : b$ is $b : a$
$\therefore$ reciprocal ratio of $39 : 41$ is $41 : 39$

$a : b = 1 : 1$ and $b : c = 81 : 24$
$\therefore \dfrac {a}{b} \times \dfrac {b}{c} = \dfrac {1}{1} \times \dfrac {81}{24} = \dfrac {27}{8}$
$\therefore a : c = 27 : 8$
$\therefore$ The subtriplicate ratio of $27 : 8$ is $\sqrt [3]{27} : \sqrt [3]{8} = 3 : 2$

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.