Question

Find the cube root of the rational number 10648/12167

Answer 1

Answer:

22/23

Step-by-step explanation:

So we that 22^3 = 10648

And 23^3 = 12167

HENCE CUBE ROOT OF 10648/12167 = 22/23

HOPE IT HELPS PLZ MARK AS BRAINLEIST

Answer 2

$\huge\red\star{{Hello}}$

$\huge\mid\mathscr\red{Answer}$

Let us consider the following rational number

$\frac{10648}{12167}$

Now,

$\sqrt[3]{\frac{10648}{12167}}$

$\frac{\sqrt[3]{10648}}{\sqrt[3]{12167}}$ (:$[\sqrt[3]{\frac{a}{b}}= \frac{\sqrt[3]{a}}{\sqrt[3]{b}}$

Cube roots by factors

On factorising 10648 into prime factors, we get:

$\[10648=\left\{2\times 2\times 2\times \right\}\times\left\{11 \times 11\times 11 \right \}$

On grouping the factors in triplets of equal factors, we get :

$\[1068 =\left\{2 \times 2 \times 2 \times \right\}\times \left \{11 \times 11 \times 11 \times\right\}$

Now, taking one factors from each triple, we get

$\sqrt[3]{12167}}$ = $\ 2 \times 11 =22$

Also factorising 12167 into prime factor, we get

12167 = ${\23 \times 23 \times 23}}$

Now getting one factor from the triple, we get:

$\sqrt[3]{12167}$ =23

Now,

$\sqrt[3]\frac{10648}{12167}$

= $\frac{\sqrt[3]{10648}}{\sqrt[3]{12167}}$

= $\frac{22}{23}$

$<marquee scrollamount=500>❣️Hope it's helps you❣️$