Tips and tricks to find square and square roots of Two or three digit number, explain it properly.
Answers
Answered by
8
Ok I know some tricks of two digit numbers:
First trick
Square of numbers between 80 and 103:
Above 100
103²=10609
- 103+3=106
- 3²=09
- Combine them 103²=10609
106²=11236
- 106+6=112
- 6²=36
- Combine again
Below 100
97²=9409
- 100-97=3
- 97-3=94
- 3²=09
- Combine
95²=9025
- 100-95=5
- 95-5-90
- 5²=25
- Combine
Second trick
ending with 5 within 100
Suppose 65²=3025
- 6*(6-1)=6*5=30
- 30 and 5² =25
- Combine
95²=9025
- 9*10=90
- 5²=25
- Combine
I knew many other tricks.
Just forgot them now.
If I remember I will surely help you again.
Hope it helps
Answered by
7
Hlo mate :-
Solution :-
● There are some tricks :-
___________________________________________________________________________________________________________________________________________________
☆ First add the last digit (2) to the number itself: 32 + 2 = 34.
■ Multiply the sum by the first digit: 34 × 3 = 102.
■Square the last digit: 2² = 4.Append that square to the product just computed: 1024.
■ If the square is a 2-digit number, append its last digit and carry the first digit to the last digit of the product.
_________________________________________________
●Why does this work?
Let the number be N = 10a + b.
(10a + b)²= 100a² + 20ab + b² = 10a(10a + 2b) + b² = 10a(10a + b + b) + b² = 10a(N + b) + b².
So, to compute the square of N = 10a + b, first find N + b. Then multiply that by the first digit a to get a(N + b). Square the second digit to get b². "Appending b²" mean multiplying a(N + b) by 10 and adding b².
In fact the method is not restricted to 2-digit numbers. a may have 2 or more digits as well. The calculations become more complex of course.
Find 215². 215 + 5 = 220. 220 × 21 = 4400 + 220 = 4620. 5² = 25. 4620·10 + 25 = 46225
___________________________________________________________________________________________________________________________________________________
☆ ☆ ☆ Hop It's helpful ☆ ☆ ☆
Solution :-
● There are some tricks :-
___________________________________________________________________________________________________________________________________________________
☆ First add the last digit (2) to the number itself: 32 + 2 = 34.
■ Multiply the sum by the first digit: 34 × 3 = 102.
■Square the last digit: 2² = 4.Append that square to the product just computed: 1024.
■ If the square is a 2-digit number, append its last digit and carry the first digit to the last digit of the product.
_________________________________________________
●Why does this work?
Let the number be N = 10a + b.
(10a + b)²= 100a² + 20ab + b² = 10a(10a + 2b) + b² = 10a(10a + b + b) + b² = 10a(N + b) + b².
So, to compute the square of N = 10a + b, first find N + b. Then multiply that by the first digit a to get a(N + b). Square the second digit to get b². "Appending b²" mean multiplying a(N + b) by 10 and adding b².
In fact the method is not restricted to 2-digit numbers. a may have 2 or more digits as well. The calculations become more complex of course.
Find 215². 215 + 5 = 220. 220 × 21 = 4400 + 220 = 4620. 5² = 25. 4620·10 + 25 = 46225
___________________________________________________________________________________________________________________________________________________
☆ ☆ ☆ Hop It's helpful ☆ ☆ ☆
Similar questions