Question

cube root of 16*90*50*24​

Answer 1

Step-by-step explanation:

The value of the cube root of 16 rounded to 5 decimal places is 2.51984. It is the real solution of the equation x3 = 16. The cube root of 16 is expressed as ∛16 or 2 ∛2 in the radical form and as (16)⅓ or (16)0.33 in the exponent form. The prime factorization of 16 is 2 × 2 × 2 × 2, hence, the cube root of 16 in its lowest radical form is expressed as 2 ∛2.

Answer 2

Solution :-

In order to find cube root of 16 * 90 * 50 * 24 , lets write given number in multiples of prime factors :-

So,

→ 16 = 2 * 2 * 2 * 2

→ 90 = 2 * 3 * 3 * 5

→ 50 = 2 * 5 * 5

→ 24 = 2 * 2 * 2 * 3

then,

→ 16 * 90 * 50 * 24 = 2 * 2 * 2 * 2 * 2 * 3 * 3 * 5 * 2 * 5 * 5 * 2 * 2 * 2 * 3 .

→ 16 * 90 * 50 * 24 = 2⁹ * 3³ * 5³

now we know that, for cube root , prime factors should be in pair of three .

therefore, making them in pair of three we get,

→ 16 * 90 * 50 * 24 = (2 * 2 * 2) * (2 * 2 * 2) * (2 * 2 * 2) * (3 * 3 * 3) * (5 * 5 * 5)

now, for cube root, taking one digit from each pair of 3 we get,

→ Required cube root = 2 * 2 * 2 * 3 * 5

→ Required cube root = 120 (Ans.)

Verification :-

→ 16 * 90 * 50 * 24 = (120)³

→ 1728000 = 120 * 120 * 120

→ 1728000 = 1728000

Learn more :-

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