Find the cube root of the result obtained when you subtract x^3 from 4

1.	Find the cube root of the result obtained when you subtract x^3 from 4097x^3 ?
Answer» Given : x³ is subtracted from 4097x³ To find : Cube root of results obtained by doing operation. Solution : First of all LET us find result of operation. ➝ 4097x³ - x³ ➩ x³(4097-1) ➩ 4096x³ ________________________________ Now we will find cube root of 4096x³ by prime factorization. ➝ 4096x³ ➩ 4096x³ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × x × x × x Now we will make pair of 3 for each NUMBER. ➩ 4096x³ = ( 2×2×2 ) × ( 2×2×2 ) × ( 2×2×2 ) × ( 2×2×2 ) × ( x×x×x ) ➩ 4096x³ = ( 2³) × ( 2³ ) × ( 2³ ) × ( 2³ ) × ( x³ ) Therefore cube root of 4096x³ will be $\sf \implies\: \sqrt[3]{4096 {x}^{3} } = \sqrt[3]{( {2}^{3} ) \times ( {2}^{3} ) \times ( {2}^{3}) \times ( {2}^{3} ) \times ( {x}^{3} ) }$ Now as it is cube root, therefore number with power 3 will be taken out of cube root with ONE value $\sf \implies\: \sqrt[3]{4096 {x}^{3} } = ( {2}) \times ( {2}) \times ( {2}) \times ( {2}) \times ( {x} )$ $\sf \implies\: \sqrt[3]{4096 {x}^{3} } = 16x$ ________________________________ ANSWER : 16x

Find the cube root of the result obtained when you subtract x^3 from 4097x^3 ?

Answer»

Cube root of results obtained by doing operation.

First of all LET us find result of operation.

➝ 4097x³ - x³

➩ x³(4097-1)

➩ 4096x³

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Now we will find cube root of 4096x³ by prime factorization.

➝ 4096x³

➩ 4096x³ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × x × x × x

Now we will make pair of 3 for each NUMBER.

➩ 4096x³ = ( 2×2×2 ) × ( 2×2×2 ) × ( 2×2×2 ) × ( 2×2×2 ) × ( x×x×x )

➩ 4096x³ = ( 2³) × ( 2³ ) × ( 2³ ) × ( 2³ ) × ( x³ )

Therefore cube root of 4096x³ will be

$\sf \implies\: \sqrt[3]{4096 {x}^{3} } = \sqrt[3]{( {2}^{3} ) \times ( {2}^{3} ) \times ( {2}^{3}) \times ( {2}^{3} ) \times ( {x}^{3} ) }$

Now as it is cube root, therefore number with power 3 will be taken out of cube root with ONE value

$\sf \implies\: \sqrt[3]{4096 {x}^{3} } = ( {2}) \times ( {2}) \times ( {2}) \times ( {2}) \times ( {x} )$

$\sf \implies\: \sqrt[3]{4096 {x}^{3} } = 16x$

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