Question

find cube root by prime factorisation
1728
15625​

Answer 1

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow 1728$

$\sf\dashrightarrow 15625$

$\large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow THE\:CUBE\:ROOTS\:BY\:PRIME\:FACTORISATION$

$\large\underline\bold{SOLUTION,}$

✯FOR, 1728,

2|1728

2|864

2|432

2|216

2|108

2|54

3|27

3|9

3|3

.|1

$\sf\implies \sqrt[3]{2\times 2\times 2 \times 2 \times2\times 2 \times 3 \times3 \times 3}$

$\sf\implies \sqrt[3]{(2\times 2\times 2) \times (2 \times2\times 2) \times (3 \times3 \times 3)}$

$\sf\implies \sqrt[3]{2^3 \times 2^3 \times 3^3}$

$\sf\implies 2 \times 2 \times 3$

$\sf\implies 12$

$\large{\boxed{\bf{ \star\:\: \sqrt[3]{1728}= 12\:\: \star }}}$

✯FOR , 15625,

5|15625

5|3125

5|625

5|125

5|25

5|5

. |1

$\sf\implies \sqrt[3]{5\times 5\times 5 \times 5 \times 5 \times 5 }$

$\sf\implies \sqrt[3]{(5\times 5\times 5 )\times (5 \times 5 \times 5) }$

$\sf\implies \sqrt[3]{5^3 \times 5^3 }$

$\sf\implies 5 \times 5$

$\sf\implies 25$

$\large{\boxed{\bf{ \star\:\: \sqrt[3]{15625}= 25\:\: \star }}}$

$\rm\underline\bold{THE\:CUBEROOTS\:OF\:THE\:GIVEN\:VALUES\:IS,\sqrt[3]{1728}= 12,\sqrt[3]{15625}= 25}$

_____________________

Answer 2

Answer:

1) 12

2) 25

Step-by-step explanation:

1)  2 | 1728

   2 |  864

   2 |  432

   2 |  216

   2 |  108

   2 |   54                                                          

   3 |   27

   3 |   9

   3 |   3    

          1

1728 = 2 ˣ 2 ˣ 2  ˣ 2 ˣ 2 ˣ 2  ˣ  3 ˣ 3 ˣ 3

$\sqrt[3]{1728}$ = 2 ˣ 2 ˣ 3 = 12

∴ $\sqrt[3]{1728}$  =  12

2)  5 | 15625​

    5 |    3125

    5 |      625

    5 |      125    

    5 |        25

    5 |          5

                   1

15625​ = 5 ˣ 5 ˣ 5  ˣ  5 ˣ 5 ˣ 5

$\sqrt[3]{15625}$ = 5 ˣ 5 = 25

∴ $\sqrt[3]{15625}$ = 25