Sarthaks Test
0 votes
82 views
in Mathematics by (15.0k points)

For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square number. Also find the square root of the square number so obtained.

(i) 2800  (ii) 1620

1 Answer

0 votes
by (24.8k points)
selected by
 
Best answer

(i) 2800 can be factorised as follows.

22800
21400
2700
2350
5175
535
77
1

2800 = 2 x 2 x 2 x 2 x 5 x 5 x 7

Here, prime factor 7 does not have its pair. If we divide this number by 7, then the number will become a perfect square. Therefore, 2800 has to be divided by 7 to obtain a perfect square.

2800 ÷7 = 400 is a perfect square

400 = 2 x 2 x 2 x2 x 5 x 5

∴ √ 400 = 2 x 2 x 5 = 20

(ii) 1620 can be factorised as follows.

21620
2810
3405
3135
345
315
55
1

1620 = 2 x 2 x 3 x 3 x 3 x 3 x 5

Here, prime factor 5 does not have its pair. If we divide this number by 5, then the number will become a perfect square. Therefore, 1620 has to be divided by 5 to obtain a perfect square.

1620 ÷5 = 324 is a perfect square.

324 =  2 x 2 x 3 x 3 x 3 x 3 

∴ √324 = 2 x 3 x 3 = 18

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

...