Question

Find the cube root of 110592 by estimation

Answer 1

Answer:

Let the numbers be 2xcube, 3xcube,4xcube

So, 2xcube+3xcube+4xcube=33957

=8xcube+27xcube+64xcube=33957

=99xcube=33957

=xcube=33957÷99

=xcube=343

=x=343cube root

=7

=2×7=14

=3×7=21

=4×7=28

Answer 2

Given:

$\bold{\sqrt[3]{110592} }$

To find:

Cube root=?

Solution:

$\Rightarrow \sqrt[3]{110592}$

Applying prime factorization:

$\Rightarrow \sqrt[3]{110592}=\sqrt[3]{2^{12} \times 3^3 }$

                   $=\sqrt[3]{2^{12} \times 3^3 }\\\\=\sqrt[3]{2^{4} \times 3^1 }\\\\=2^{4} \times 3^1 \\\\=16 \times 3\\\\=48$

The final value is: 48