Question

what is the smallest number by what 2560 must be multiplied so that it is a perfect square.. ?

Answer 1

GivEn:

• Number = 2560

To find:

• The least number it must be multiplied with.

Solution:

• First let's do prime factorization of the given number.

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

« Now, Finding prime factors,

• Prime factors are,

→ 9075 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5

• Let's make pairs from the factors obtained.

• (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × 2 × 5

Here, As we can see, 2 and 5 are not in any pair.

Thus, We can conclude that 2560 must be multiplied with 10 to get a perfect square.

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

« Now, Finding the new number,

→ 2560 × 10

→ √25600

→ 160

∴ Hence, The new number is 160.

Answer 2

$\huge\red{\mid{\fbox{\tt{Given:}}\mid}} \:$

◆ Number = 2560

$\huge\red{\mid{\fbox{\tt{To \: Find:}}\mid}} \:$

◆ The smallest number it must be multiplied.

$\huge\red{\mid{\fbox{\tt{Solution:}}\mid}} \:$

✠ To do this question we will do Prime Factorisation of the given number 2560.

______________________________

✠ Let's find the Prime Factors,

• Refer to the attachment

‣ Prime Factors are:

• (2 X 2) X (2 X 2) X (2 X 2) X (2 X 2) X 2 X 5
• 2 and 5 are unpaired
• So, 2 and 5 should be multiplied
• 2 X 5 = 10

Thus, 10 should be multiplied to get a perfect square.

>> Now let's find the new number,

↪ 2560 X 10

↪ 25600

>> Now let's find the square root of the new number :

❖ √25600

❖ 160

∴ 10 should be multiplied with 2560 to get a perfect square and the new number is 160.