Question

Which of the following expressions is not a perfect cube? *

1 point

5 x 10 x 32X 3

125 x 8 x 125

15 x 8 x 25 x 9

49 x 21 x 27 x 8

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Answer 1

Step-by-step explanation:

Hiii!!

1.

=> 5 * 10 * 32 * 3 = 5 * 5 * 2 * 2^5 * 3 = 5^2 * 2^6 * 3

THIS IS NOT A PERFECT CUBE.

2.

=> 125 * 8 * 125 = 5^3 * 2^3 * 5^3 = 25^3 * 2^3.

THIS IS A PERFECT CUBE.

3.

=> 15 * 8 * 25 * 9 = 3 * 5 * 2^3 * 5^2 * 3^2 = 2^3 * 3^3 * 5^3.

THIS IS A PERFECT CUBE.

4.

=> 49 * 21 * 27 * 8 = 7^2 * 3 * 7 * 3^3 * 2^3 = 7^3 * 3^4 * 2^3

THIS IS NOT A PERFECT CUBE.

HOPE IT HELPS!!!!

PLS THNK MY ANSWERS!!!!

Answer 2

1. Resolve (5×10×32×3 ) into prime factors ,we get

5×10×32×3

= 5 × 2 × 5 × 2×2×2×2×2×3

= 2×2×2× 2×2×2 ×3 × 5×5

The prime factors 3 and 5 doesn't appear in a group of three.

So, 5×10×32×3 is not a perfect cube.

2. Resolve (125 × 8 × 125 ) into prime factors ,we get

125 × 8 × 125

= 5 × 5 × 5 × 2 × 2 × 2 × 5 × 5 × 5

Each factor appear three times .

Therefore.,

So, (125 × 8 × 125 ) is a perfect cube .

$125 \times 8 \times 125 \\= ( 5 \times 2 \times 5)^{3}\\= (50)^{3} \: \pink{ ( Perfect \:cube ) }$

3. Resolve (15 × 8 × 25 × 9 ) into prime factors ,we get

15 × 8 × 25 × 9

= 3 × 5 × 2 × 2 × 2 × 5 × 5 × 3 × 3

= 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5 × 5

Each factor appear three times .

Therefore.,

So, (15 × 8 × 25 × 9 ) is a perfect cube .

$15 \times 8 \times 25\times 9 \\= ( 2 \times 3 \times 5)^{3}\\= (30)^{3} \: \pink{ ( Perfect \:cube ) }$

4. Resolve (49 × 21 × 27 × 8 ) into prime factors ,we get

49 × 21 × 27 × 8

= 7 × 7 × 3 × 7 × 3× 3 × 3 × 2 × 2 × 2

= 2 × 2 × 2 × 3 × 3 × 3 × 3 × 7 × 7 × 7

The prime factor 3 doesn't appear in a group of three .

Therefore.,

So, (49 × 21 × 27 × 8 ) is not a perfect cube .

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