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Class 10MathematicsReal NumbersPrime FactorisationExpertLevel 7

If a number has prime factorisation (2^9\times3^6\times7^3), what is its cube root?

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Answer and explanation

Correct answer: (2^3\times3^2\times7)

Step 1: For cube root, divide each prime exponent by (3). Step 2: (9\div3=3), (6\div3=2), and (3\div3=1), so the cube root is (2^3\times3^2\times7). Step 3: In a perfect cube, all exponents are multiples of (3).

Tags

real numberscube rootprime factorisationperfect cube

Frequently asked questions

What is the correct answer to this question?

(2^3\times3^2\times7)

Why is this the correct answer?

Step 1: For cube root, divide each prime exponent by (3). Step 2: (9\div3=3), (6\div3=2), and (3\div3=1), so the cube root is (2^3\times3^2\times7). Step 3: In a perfect cube, all exponents are multiples of (3).

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Prime Factorisation.

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