Question

3
$3 \sqrt{4 \times 3 \sqrt{16} }$
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Answer 1

Answer:

$\sqrt[3]{4 \times 3 \sqrt{16} } \\ = \sqrt[3]{4 \times 3 \times 4} \\ = \sqrt[3]{48} \\ = \sqrt[3]{(2 \times 2 \times 2) \times 2 \times 3} \\ = 2\sqrt[3]{6} \: \: or \: \: 3.6342$

Cube Root of 48

The value of the cube root of 48 rounded to 5 decimal places is 3.63424. It is the real solution of the equation x3 = 48. The cube root of 48 is expressed as ∛48 or 2 ∛6 in the radical form and as (48)⅓ or (48)0.33 in the exponent form. The prime factorization of 48 is 2 × 2 × 2 × 2 × 3, hence, the cube root of 48 in its lowest radical form is expressed as 2 ∛6.

Cube root of 48: 3.634241186

Cube root of 48 in Exponential Form: (48)⅓

Cube root of 48 in Radical Form: ∛48 or 2 ∛6

Cube Root of 48

What is the Cube Root of 48?

The cube root of 48 is the number which when multiplied by itself three times gives the product as 48. Since 48 can be expressed as 2 × 2 × 2 × 2 × 3. Therefore, the cube root of 48 = ∛(2 × 2 × 2 × 2 × 3) = 3.6342.

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How to Calculate the Value of the Cube Root of 48?

Cube Root of 48 by Halley's Method

Its formula is ∛a ≈ x ((x3 + 2a)/(2x3 + a))

where,

a = number whose cube root is being calculated

x = integer guess of its cube root.

Here a = 48

Let us assume x as 3

[∵ 33 = 27 and 27 is the nearest perfect cube that is less than 48]

⇒ x = 3

Therefore,

∛48 = 3 (33 + 2 × 48)/(2 × 33 + 48)) = 3.62

⇒ ∛48 ≈ 3.62

Therefore, the cube root of 48 is 3.62 approximately.

Answer 2

Answer:

$3 \sqrt{4 \times 3 \sqrt{16} } \\ = 3 \sqrt{4 \times 3 \times 4} \\ = 3 \sqrt{48} \\ = 3 \times 4 \sqrt{3} \\ = 12 \sqrt{3} \\ \\ \\ \\ \\ this \: is \: your \: answer \\ hope \: this \: helps \: you$

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