Question

Find the cube root of the following numbers by prime factorization method.
(i) 343
(ii) 729
(iii) 1331
(iv) 2744

Answer 1

Solution :

i ) 343 = 7 × 7 × 7

cube root of 343 = ( 7³ )^1/3 = 7

ii ) 729 = 3 × 3 × 3 × 3 × 3 × 3

cube root of 729 = ( 3^6 )^1/3 = 3² = 9

iii ) 1331 = 11 × 11 × 11

cube root of 1331 = ( 11³ )^1/3 = 11

iv ) 2744 = 2 × 2 × 2 × 7 × 7 × 7

= 2³ × 7³

Cube root of 2744 = ( 2³ × 7³ )^1/3

= [ ( 2 × 7 )³ ]^1/3

= 2 × 7

= 14

••••

Answer 2

( i )

343 = 7 × 7 × 7

343 = 7³



So, cube root of 343 = ³√343

cube root of 343 = ³√{ 7³ }

cube root of 343 = 7




( ii )

729 = 9 × 9 × 9

729 = 9³



So, cube root of 729 = ³√729

cube root of 729 = ³√{ 9³ }

cube root of 729 = 9




( iii )

1331 = 11 × 11 × 11

1331 = 11³



So, cube root of 1331 = ³√1331

cube root of 1331 = ³√{ 11³ }

cube root of 1331 = 11




( iv )

2744 = 14 × 14 × 14

2744 = 14³



So, cube root of 2744 = ³√2744

cube root of 2744 = ³√{ 14³ }

cube root of 2744 = 14

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