Question

Cube root of 13824 by primefactorisation method

Answer 1

13824= 2*2*2*2*2*2*2*2*2*3*3*3

2*2*2*3= 24

Answer 2

Answer:

$Cube \: root \: of \: 13824\\=\sqrt[3]{13824}=24$

Step-by-step explanation:

Resolving given number 13824 into product of prime factors.

2| 13824

_________

2| 6912

_________

2| 3456

_________

2| 1728

_________

2| 864

_________

2| 432

_________

2| 216

_________

2| 108

_________

2| 54

_________

3| 27

_________

3| 9

_________

*** 3

$Cube \: root \: of \: 13824\\=\sqrt[3]{13824}\\=\sqrt[3]{2^{9}\times 3^{3}}\\=\sqrt[3]{(2^{3}\times 3)^{3}}\\=\sqrt[3]{(8\times 3)^{3}}\\=(24)^{\frac{3}{3}}\\=24$

Therefore,

$Cube \: root \: of \: 13824\\=\sqrt[3]{13824}=24$

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