Question

the cube root of 1.728 is​

Answer 1

Cube root of=³√1.728

=³√1728/1000

=³√12³/10³

= 1.2

Answer 2

Answer:

The value of cube root of 1.728 is$1 \frac{1}{5}$

Step-by-step explanation:

Here we want find cube root of 1.728.

Now question is what is the meaning of cube root?

Cube root of x

$= \sqrt[3]{x} = {x}^{ \frac{1}{3} }$

Here x=1.728

So,cube root of 1.728

$= \sqrt[3]{1.728} \\ = {1.728}^{ \frac{1}{3} } \\ = ( { \frac{1728}{1000} )}^{ \frac{1}{3} } \\ = ({ \frac{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3}{2 \times 2 \times 2 \times 5 \times 5 \times 5} })^{ \frac{1}{3} } \\ = ({ \frac{ {2}^{6} \times {3}^{3} }{ {2}^{3} \times {5}^{3} } })^{ \frac{1}{3} } \\ = \frac{ {2}^{2} \times 3}{2 \times 5}$

$= \frac{2 \times 3}{5} \\ = \frac{6}{5}$

Required value of cube root of 1.728 is $\frac{6}{5} = 1 \frac{1}{5}$

Here applied formula,

$x \times x \times x.....n \: \: times \: = {x}^{n}$

${x}^{ {a}^{ \frac{1}{a} } } = {x}^{a \times \frac{1}{a} } = {x}^{1} = x$