Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
7.5k views
in Mathematics by (15.0k points)

Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.

(i) 252 (ii) 1825 (ii) 6412

1 Answer

0 votes
by (24.9k points)
selected by
 
Best answer

(i) The square root of 252 can be calculated by long division method as follows.

The remainder is 27. It represents that the square of 15 is less than 252. The next number is 16 and 162 = 256 Hence, number to be added to 252 = 162 − 252 = 256 − 252 = 4 The required perfect square is 256 and 256 = 16

(ii) The square root of 1825 can be calculated by long division method as follows.

The remainder is 61. It represents that the square of 42 is less than 1825. The next number is 43 and 432 = 1849 Hence, number to be added to 1825 = 432 − 1825 = 1849 − 1825 = 24 The required perfect square is 1849 and 1849 = 43

(iii) The square root of 6412 can be calculated by long division method as follows.

The remainder is 12. It represents that the square of 80 is less than 6412. The next number is 81 and 812 = 6561 Hence, number to be added to 6412 = 812 − 6412 = 6561 − 6412 = 149 The required perfect square is 6561 and 6561 = 81

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...