cube of 1000 has how many zeros?
Answers
Answer:
<span lang="EN-US. We know that by law of exponents, (am)n = amn. Hence, there is only one zero in the cube root of 1000.
Step-by-step explanation:
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Answer:
The value of the cube root of 1000 is 10. It is the real solution of the equation x3 = 1000. The cube root of 1000 is expressed as ∛1000 in radical form and as (1000)⅓ or (1000)0.33 in the exponent form. As the cube root of 1000 is a whole number, 1000 is a perfect cube.
Cube root of 1000: 10
Cube root of 1000 in exponential form: (1000)⅓
Cube root of 1000 in radical form: ∛1000
What is the Cube Root of 1000?
The cube root of 1000 is the number which when multiplied by itself three times gives the product as 1000. Since 1000 can be expressed as 2 × 2 × 2 × 5 × 5 × 5. Therefore, the cube root of 1000 = ∛(2 × 2 × 2 × 5 × 5 × 5) = 10.
How to Calculate the Value of the Cube Root of 1000?
Cube Root of 1000 by Prime Factorization
Prime factorization of 1000 is 2 × 2 × 2 × 5 × 5 × 5
Simplifying the above expression: 23 × 53
Simplifying further: 103
Therefore, the cube root of 1000 by prime factorization is (2 × 2 × 2 × 5 × 5 × 5)1/3 = 10.
Is the Cube Root of 1000 Irrational?
No, because ∛1000 = ∛(2 × 2 × 2 × 5 × 5 × 5) can be expressed in the form of p/q i.e. 10/1. Therefore, the value of the cube root of 1000 is an integer (rational).