Question

please answer the above questions and show the proper solution how you solved it please answer all the questions please​

Answer 1

Answer:

thankyou IIMYSTERIOUSII for answering my questions thanks a lott you helped me a lot thanks a lot dear purple you forever:)

♥♥♥♥♥and good morning Tina!!!

Answer 2

$\huge\text{Question}$

1) find the cube root of the following :

(i) 85184 = 44

(ii) 21952 = 28

(iii) 42875 = 35

(iv) 35937 = 32

(v) 46656 = 36

(vi) 74088 = 42

(vii) 59319 = 39

(viii) 110592 = 49

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$\huge\text{Question}$

2) By which smallest number should we multiply the following numbers to make them perfect cubes ? Find the cube root of the perfect cube .

(i) 30375

Prime factorising 30375, we get,

30375 = 3 × 3 × 3 × 3 × 3 × 5 × 5 × 5

30375 = 3³ × 5³ × 3²

We know, a perfect cube has multiples of 3 as powers of prime factors. Here, we can see that power of 3 is 3 and power of 5 is 3 and the power of other 3 is 2 .

so , The smallest number 3 should be multiply by 30375 to make it perfect cube .

30375 × 3 = 91125

Cube root of 91125 = 45

(ii) 43200

Prime factorising 43200, we get,

43200 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5

43200 = 2³ × 2³ × 3³ × 5²

We know, a perfect cube has multiples of 3 as powers of prime factors. Here, we can see that power of both 2 is 3 and power of 3 is 3 and the power of 5 is 2.

so , The smallest number 5 should be multiply by 43200 to make it perfect cube .

43200 × 5 = 216000

Cube root of 216000 = 60

(iii) 16384

Prime factorising 16384, we get,

16384=2×2×2×2×2×2×2×2×2×2×2×2×2×2

16384= 2³ × 2³ × 2³ × 2³ × 2²

We know, a perfect cube has multiples of 3 as powers of prime factors. Here, we can see that power of all 2 is 3 except one 2 whose power is 2.

so , The smallest number 2 should be multiply by 200704 to make it perfect cube .

16384 × 2 = 32768

Cube root of 32768 = 32

(iv) 24000

Prime factorising 24000, we get,

24000 = 2× 2× 2 ×2 ×2× 2 × 5 × 5 × 5 × 3

24000 = 2³ × 2³ × 5³ × 3¹

We know, a perfect cube has multiples of 3 as powers of prime factors. Here, we can see that power of both 2 is 3 and power of 5 is 3 and the power of 3 is 1.

so , The smallest number 9 should be multiply by 24000 to make it perfect cube .

24000 × 9 = 216000

Cube root of 216000 = 60

(v) 145800

Prime factorising 145800, we get,

145800 = 2 × 2 × 2 × 5 × 5 × 3 × 3 × 3 × 3 × 3 × 3

145800 = 2³ × 3³ × 3³ × 5²

We know, a perfect cube has multiples of 3 as powers of prime factors. Here, we can see that power of 2 is 3 and power of both 3 is 3 and power of 5 is 2.

so , The smallest number 5 should be multiply by 145800 to make it perfect cube .

145800 × 5 = 729000

Cube root of 729000 = 90