Question

what least number must be subtracted from 16160 to get a perfect square ? also find the square root of this perfect square​

Answer 1

Answer:

31 should be subtracted.

Step-by-step explanation:

16160-31= 16129

$\sqrt{16129} = 271$

Answer 2

✹ Question ✹

What least number must be subtracted from 16160 to get a perfect square? Also find the square root of this perfect square.

✹ To find ✹

• The least number to be added.
• Square root of the perfect square.

✹ Solution ✹

First we have to find the root of 16160 by long division method.

 1 ) 16160   ( 127

    1      

22 )  61

      44  

247 )  1760

1729

31

So, we can see that 16160 > (127)² by 31.

(127)² = (127 × 127) = 16129

We can see 16129 is a perfect square and is less than 16160.

Let the number to be added to 16160 to get 16129 be x.

According to condition,

16160 - x = 16129

⇒ -x = 16129 - 16160

⇒ -x = -31

⇒ x = 31

✹ Hence ✹

• The number to be subtracted = 31
• The root of the perfect square = √16129 = 127

✹ Therefore ✹

• 31 is the least number that must be subtracted from 16160 to make it a perfect square.
• The root of the perfect square is 127.

   

๑ Hope this helps you. ๑