Question

find the least number which must be subtracted from 6000 numbers so as to get a perfect square. also find the square root of the perfect square so obtained.

Answer 1

Answer:

To find the least number that must be subtracted from 6203 to obtain a perfect square, we will have to compute the square root of 6203 by Long Division method. So, the remainder is 119 and 119 is the least number that must be subtracted from 6203 to get a perfect square.

Step-by-step explanation:

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Answer 2

Answer:

71 is the least number which will be subtracted from 6000 to get a perfect square and 77 is the square root of the perfect square so obtained.

Step-by-step explanation:

To find:-

(a) The least number that must be subtracted from 6000 to get a perfect square.

(b) Find the square root of the perfect square so obtained.

(a) Consider the given number as follows:

6000

Compute the square of the number 6000 as follows:

$\sqrt{6000} = \sqrt{2\times2\times2\times2\times5\times 5\times5\times 3}$

          $=2\times 2\times5\times\sqrt{5\times3}$

          $=20\sqrt{15}$

The value of $\sqrt{15}=3.87$.

So,

$\sqrt{6000}=20\times3.87$

          $=77.4$

Now, find the square of the number 77 as follows:

$77^2=77\times 77$

     $=5929$

Lastly, subtract the numbers 6000 and 5929 as follows:

⇒ $6000-5929$

⇒ $71$

Thus, 71 is the least number which will be subtracted from 6000 to get a perfect square.

(b)The perfect square number so obtained is 5929.

The square root of 5929 is,

$=\sqrt{5929}$

$=\sqrt{77\times 77}$

$=77$

Therefore, 77 is the required square root.

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