Question

Find the smallest number by which 675 must be multiplied to obtain a perfect cube.

Answer 1

Answer:

5

Step-by-step explanation:

675×5= 3375

3375 is a perfect cube

Please mark as brainlist answer

Answer 2

The smallest number by which 675 must be multiplied to obtain a perfect cube is 5.

Concept :

Perfect cube:

• The cube of a number is that number raised to the power 3.
• As we know that 2³ = 8 , 3³ = 27, 4³ = 64 , 5³ = 125 ….
• The numbers  8, 27, 64, and 125 are called perfect cubes.
• The natural number n is perfect if there exists a natural number m such that m × m × m = n.

Given :

Number is = 675

To find :

The smallest number by which 675 must be multiplied to obtain a perfect cube.

Solution :

Step 1 :

Resolving 675 into prime factors:

675 = 5 × 5 × 3 × 3 × 3

Step 2 :

Grouping the factor in triplets of equal factors

675 = 5 × 5 × (3 × 3 × 3)

Here, two 5s are left which are not in a triplet.

To make 675 a cube, one more 5 is required. so, we multiply 675 by 5 to make it a perfect cube.

675 × 5 = (3 × 3 × 3 ) × (5 × 5 × 5 ) = 3375 is a perfect cube.

Hence, the smallest number by which 675 must be multiplied to obtain a perfect cube is 5.

Learn more on Brainly :

Which of the following is both a perfect square and a perfect cube? 16 64 125 144

https://brainly.in/question/19313913?msp_srt_exp=6

Question 3 Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube. (i) 81 (ii) 128 (iii) 135 (iv) 192 (v) 704

https://brainly.in/question/1449143?msp_srt_exp=6

#SPJ3