Question

Find the smallest number which we get by multiplying it with 100 to get perfect
cube.
3
Write a Pythagorean triplet whose one number is 12.
step by step​

Answer 1

Answer:

....

Step-by-step explanation:

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Answer 2

Part - I

To find:

✠ The smallest number which we get by multiplying it with 100 to get perfect cube.

Solution:

Let's understand the concept first!

• A perfect cube has three as powers of the prime factors.
• In this question, the power of 2 is 2s and that of 5 is also 2s ( 2² and 5² )
• We need to multiply 2 and 5 further to obtain the smallest number to make perfect cube of 100 by multiplying it with 100. So, it will be 2 × 5 = 10

Let's find out...✧

By prime factorization method,

2 | 100

2 | 50

5 | 25

5 | 5

| 1

➛ 2 × 2 × 5 × 5

➛ 2 × 2 × 5 × 5

➛ 2 × 5 = 10

∴ 100 should be multiplied by 2 × 5 = 10 to get perfect cube.

Part - II

To find:

✠ A Pythagorean triplet whose one number is 12.

Solution:

We know that in the Pythagoras triplet in general form is 2m, m² - 1 and m² + 1

We know that one number in a Pythagorean triplet is 12.

So, Let us take

➤ 2m = 12

➤ m = 12/2

➤ m = 6

Now, find a Pythagorean triplet

➛ m² - 1

➛ 6² - 1

➛ 36 - 1

➛ 35

➛ m² + 1

➛ 6² + 1

➛ 36 + 1

➛ 37

∴ The required Pythagorean triplet is 12, 35 and 37.

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