Question

find the cube rootof4741632 by estimation​

Answer 1

$\huge{\sf{\underline{Solution:}}}$

Write 4741632 as: $\boxed{\sf{4.741632 \times 10^{6}}}$

$\sf{\underline{Such\:that:}}$

The power of 10 is a multiple of 3.

$\sf{\underline{Find\:the:}}$

$\implies$ Cube root of 4.741632.

$\implies$ Cube root of $\sf{10^{6}}$ is $\sf{10^{2}}$

$\sf{\underline{Multiply\:A\:and\:B:}}$

To find the Cube root of 4.741632 :

$\sf{\underline{Estimate\:is\:2:}}$

Express the number as a multiple of:

$\boxed{\sf{2\times 2}}$

$\boxed{\sf{4.741632=2\times 2\times 1.185408}}$

The average of the three factors is:

$\boxed{\sf{1.728469}}$

Express the number as multiple of:

$\boxed{\sf{1.7 \times 1.7}}$

$\boxed{\sf{4.741632=1.7 \times 1.7 \times 1.6407}}$

The average of the three factors is 1.68

This is a fair estimate of the cube root of 4.741632.

$\sf{\underline{Therefore:}}$

The cube root of:

$\boxed{\sf{4741632=1.68 \times 100=168}}$