Thanks for your answer to my below question, but I could not understant, how will i deceide for Question A :- that will start from 45 2 =2025 < 2361
and for Question B:- is star5ting from 125 2 =15625
Is there any trick?
I was refering R.D Sharma textbook where in Exe- 3.5 Q.no. 2 to find least no. which must be subtracted from the following no.to make them perfect square
Could you please explain me the above question.
Ans: a. 45 2 =2025 < 2361 46 2 =2116 < 2361 47 2 =2209 <2361 48 2 =2304 < 2361 49 2 =2401 > 2361 So we observe, 48 2 < 2361 < 49 2 2304 < 2361 < 2401 Hence, the minumum nunber that needs to be subtracted to make it a perfect square is 2361 - 2304 = 57 b. 125 2 =15625 < 16160 126 2 =15876 < 16160 127 2 =16129 < 16160 128 2 =16384 > 16160 So we observe, 127 2 < 16160 < 128 2 16129 < 16160 < 16384 Hence, the minumum nunber that needs to be subtracted to make it a perfect square is 16160 - 16129 = 31
Asked by divya.tripathy | 25th Jun, 2015, 11:40: AM
For part (a), since the number given is 2361, we have to find a number whose square is less than 2361.
We could have started with 40 also. We know that 402=1600. There is a huge gap between 1600 and 2361. So we can try for numbers more than 40, like 41, 42 and so on.
We can use the trick to quickly find the square of a number ending in 5. 452=2025 which is less than 2361.
Similarly for part (b), we could have started from 1202. But since 125 ends in 5 and its square can be found easily, we started from 125.
(Method to quickly find square of a number ending in 5. Let the number be "N5". We find N(N+1) and we simply place 25 to the right of that number.
For example to find square of 45, we find 4(4+1)=4*5=20, and we place 25 to the right of it. So the number becomes 2025. Hence, 452=2025.
To find the square of 125, we find 12(12+1)=12*13=156, and we place 25 to the right of it. So the number becomes 15625. Hence, 1252=15625.
Answered by satyajit samal | 26th Jun, 2015, 09:46: AM
- find the
- in a pond, a lotus flower bloomed one day.the second day,the number of flowers becomes two and the third day it becomes four.on the fourth day it becomes eight and this pattern continued.on the 15th day, the pond becomes half filled with lotus flowers.how many more days will it take for the pond to be fully flled with lotus flowers?state the number of flowers needed to fill the pond in exponential form. the area of a square field is 4096 metre squared.what is the lenght of each side?
- Find the smallest number by which 5103 must be divided to get a perfect square.
- Find the smallest number by which 882 must be multiplied so that the product becomes a perfect square.
- Is the number 2048 a perfect square? If not, then by which number it must be multiplied so as to get a perfect square.
- Find the least number that must be added to 1300 so as to get a perfect square. Also, find the square root of the perfect square so obtained.
- In a park there are 1225 trees. These trees are arranged in such a way that each row contains as many trees as the number of rows. Find the number of rows and the number of trees in each row.
- In an auditorium, the number of rows is equal to the number of chairs in each row. If the capacity of the auditorium is to accommodate 1764 chairs, find the number of chairs in each row.
- Is 90 a perfect square? If not, find the number with which it must be divided to get a perfect square number.
- Is the number 5460 a perfect square? If not, find the smallest number which needs to be subtracted from it to make it a perfect square.
Kindly Sign up for a personalised experience
- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions
Verify mobile number
Enter the OTP sent to your number