13934 square root by long division with steps WHAT IS THE SMALLEST NO. TO BE SUBTRACTED FROM 13934 TO GET A PERFECT SQUARE.. PLEASE HELP
Answers
Solution:
(i) 402
We know that, if we subtract the remainder from the number, we get a perfect square.
Here, we get the remainder 2. Therefore 2 must be subtracted from 402 to get a perfect square.
(iii) 3250
We know that, if we subtract the remainder from the number, we get a perfect square.

Here, we get the remainder 1. Therefore 1 must be subtracted from 3250 to get a perfect square.
\therefore3250-1=3249∴3250−1=3249
Hence, the square root of 3249 is 57
825
We know that, if we subtract the remainder from the number, we get a perfect square.

Here, we get remainder 41. Therefore 41 must be subtracted from 825 to get a perfect square.
\therefore825-41=784∴825−41=784
Hence, the square root of 784 is 28.


Ncert solutions
Grade 8
Mathematics
Science

Chapters in NCERT Solutions - Mathematics , Class 8

Exercises in Squares and Square Roots

Question 4

Q4) Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained:
(i) 402
(ii) 1989
(iii) 3250
(iv) 825
(v) 4000
Solution
Transcript
Solution:
(i) 402
We know that, if we subtract the remainder from the number, we get a perfect square.
Here, we get the remainder 2. Therefore 2 must be subtracted from 402 to get a perfect square.

\therefore402-2=400∴402−2=400
Hence, the square root of 400 is 20.

(ii) 1989
We know that, if we subtract the remainder from the number, we get a perfect square.

Here, we get the remainder 53. Therefore 53must be subtracted from 1989 to get a perfect square.
\therefore1989-53=1936∴1989−53=1936
Hence, the square root of 1936 is 44.

(iii) 3250
We know that, if we subtract the remainder from the number, we get a perfect square.

Here, we get the remainder 1. Therefore 1 must be subtracted from 3250 to get a perfect square.
\therefore3250-1=3249∴3250−1=3249
Hence, the square root of 3249 is 57.

(iv) 825
We know that, if we subtract the remainder from the number, we get a perfect square.

Here, we get remainder 41. Therefore 41 must be subtracted from 825 to get a perfect square.
\therefore825-41=784∴825−41=784
Hence, the square root of 784 is 28.

(v) 4000
We know that, if we subtract the remainder from the number, we get a perfect square.

Here, we get the remainder 31. Therefore 31 must be subtracted from 4000 to get a perfect square.
\therefore4000-31=3969∴4000−31=3969
Hence, the square root of 3969 is 63
(iii) 3250
We know that, if we subtract the remainder from the number, we get a perfect square.

Here, we get the remainder 1. Therefore 1 must be subtracted from 3250 to get a perfect square.
\therefore3250-1=3249∴3250−1=3249
Hence, the square root of 3249 is 57
825
We know that, if we subtract the remainder from the number, we get a perfect square.

Here, we get remainder 41. Therefore 41 must be subtracted from 825 to get a perfect square.
\therefore825-41=784∴825−41=784
Hence, the square root of 784 is 28.
\therefore402-2=400∴402−2=400