Find the cube root of 27000 by prime factorisation method.Topic Introduction to MensurationSubtopic Introduction to Mensuration

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Find the cube root of $27000$ by prime factorisation method.

Topic Introduction to Mensuration

Subtopic Introduction to Mensuration

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answer is A.

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Detailed Solution

Concept: We will find prime factors of

27000,

if it is a perfect cube and then will pair them in a group of three.

\Rightarrow 27000 = 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 5 \times 5 \times 5

On forming pairs of three
⇒ 27000=

2^{3} \times 3^{3} \times 5^{3}

Since 2, 3 and 5 occurs in triplets
27000 is a perfect cube
⇒27000=

2^{3} \times 3^{3} \times 5^{3}

It can be write like,
⇒27000=(

2^{3} \times 3^{3} \times 5^{3}

)
On cancelling exponential power
⇒

So cube root of 27000 ​ = 2 \times 3 \times 5 = 30

Hence, the final answer is option 1.

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