What is the least number that should be added to 1642 in order to obtain a perfect square?Also,find the square root of the resulting number
Answers
Answer:
39 must be added to 1642 and 41 is the square root of the resulting number.
Step-by-step explanation:
The nearest perfect square of 1642 is 1600 and 1681 which is square of 40 and 41 respectively.
But since we need to add to get the perfect square, 1600 is neglected as we need to subtract from 1642 to get 1600.
Hence 1681 is the perfect square nearest to 1642 which we get by adding.
Therefore number to be added = x
⇒ x + 1642 = 1681
⇒ x = 1681 - 1642
⇒ x = 39
Hence 39 must be added to 1642 to get a perfect square.
Square root of resulting number is √ 1681 = 41
Hence 41 is the square root of the resulting number
ANSWER⇒
39 AND 41
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Since we know
1600 and 1681 are the square of 20 and 21 respectively
We have 1642 + x = perfect square
There for 1681 is only possible becoz it can be obtained by adding something to 1642 as question needs.. We cannot subtract. To get 1600