Question

Find the cube root of 729/1000 by prime factorization method.

Answer 1

Answer:29=3*3*3*3*3*3

\sqrt[3]{729}  =  \sqrt[3]{3 \times 3 \times 3 \times 3 \times 3 \times 3}  

\sqrt[3]{729}  = 9

So, 9 is the cube root of 729

Answer 2

GIVEN :

• The number for finding cube root = 729/1000.

TO FIND :

• The cube root of 729/1000 = ?

STEP - BY - STEP EXPLANATION :

$= > \sqrt[3] \frac{729}{1000}$

$= > \frac{ \sqrt[3]{729} }{ \sqrt[3]{1000} }$

Resolving 729 and 1000 into prime factors.

$= > 729 = 3 \times 3 \times 3 \times 3 \times 3 \times 3$

=> 1000 = 2³ × 5³

$= > \sqrt[3]{729} = 3 \times 3 = 9$

$= > \sqrt[3]{1000} = 2 \times 5 = 10$

$= > hence \: \sqrt[3] \frac{729}{1000} = \frac{ \sqrt[3] 729}{\sqrt[3]{1000} } = \frac{9}{10}$

Hence, the cube root of 729/1000 = 9/10.