$\sqrt{5050^2-4950^2}=\sqrt {(5050+4950)(5050-4950) }$

$=\sqrt {(10000)(100)}=\sqrt{1000000}=\boxed{1000}$

$\sqrt{5050^2-4950^2} = \sqrt{(5000+50)^2-(5000-50)^2} \\ =\sqrt{2(5000)(50)+2(5000)(50)} \\ =\sqrt{4(5000)(50)} \\ =\sqrt{4(500)(500)} \\ =2(500)=\boxed{1000}$

$\sqrt{5050^2-4950^2}$

$=\sqrt{(5050+4950)(5050-4950)}$

$=\sqrt{(10000)(100)}$

$=\sqrt{1000000}$

$=\boxed{1000}$

$\sqrt{5050^2 - 4950^2} = \sqrt{(5000+50)^2 - (5000-50)^2} = \sqrt{2 \times 5000 \times 50 - ( - 2 \times 5000 \times 50 ) } = \sqrt{4 \times 500^2} = 2 \times 500 = \boxed{1000}$

sqrt(5050^2-4950^2) Sub x=5050

=sqrt(x^2-(x-100)^2)

=sqrt(x^2-x^2-10000+200x)

=sqrt(200x-10000)
sub x=5050 back into eq

=sqrt(200*5050-10000) =1000

10x100=1000

Since I can be fairly certain that the answer is in the set of whole numbers, I employed the factorization rule for differences of perfect squares:

$a^2 - b^2 = ( a + b ) \times ( a - b )$

$a + b = 10,000$

$a - b = 100$

Now the problem is just $\sqrt{1,000,000} = 1,000$

5050 X 5050 = 25502500
4950 X 4950 = 24502500
25502500 - 24502500 = 1000000
Square Root of 1000000 = 1000
Better don't do it manually but use the calculator

$\sqrt{5050^2-4950^2} = \sqrt{(5050-4950)^2}$ $=\sqrt{(5050+4950)(5050-4950)}$ = $\sqrt{(10000)(100)}$ = $(100)(10)$ = $1000$

I came up on my own system. √[(5050-4950)x2 x 5000] essentially double the difference and multiply the average.

You can also consider 5050 as 4950+100 so (4950+100)^2 - 4950^2 =

4950^2+10.000+200*4950 - 4950^2=10.000+990000= 1.000.000

Sqrt (1.000.000)=1.000

$let x = 5050, and hence 4950 = x - 100$

$x^2 - (x - 100)^2$

$= x^2 - (x - 100)(x - 100)$

$= x^2 - (x^2 - 200x +10000)$

$= 200x - 10000$

$200(5050) - 10000$

$= 1010000 - 10000$

$= 1000000$

$√1000000$ $= 1000$

$\sqrt{5050^{2} - 4950^{2}}$

$5050 = 4950 + 100$

$\sqrt{{4950 + 100}^{2} - 4950^{2}}$

$\sqrt{4950^{2} + 2 \cdot 4950 + 100^{2} - 4950^{2}}$

$\sqrt{990000 + 10000}$

$\sqrt{1000000 = \boxed{1000}}$

I did it making a=5000, so ((a+50)^2)-((a-50)^2) and so on...

i forget everything from 8th grade i could've solved that in 3 seconds before this summer

use (a^2 - b^2)= (a+b)(a-b)

a2-b2=(a+b)(a-b)

We can express 5050 as a and 4050 as b,so we get underroot (a+b) ( a-b) substituting values we get underroot 1000000 that is 1000 Ans

√(5050)^2-(4950)^2 = 1000 √(a2-b2) =√ (a+b)(a-b) √(10000)(100) =1000

Example : a=5050 ; b=4950 ; [(a×a)–(b×b)]^½=[(a+b)×(a–b)]^½ ; [(5050+4950)×(5050–4950]^½=[10000×100]^½=[1000000]^½=1000.

= a^{2} - b^{2} = (a-b)(a+b), where a = 5050 and b = 4950.

Substituting gives us = (5050-4950)(5050+4950) = (100)(10000)

Now place the square root = sqrt{(100)(10000)} = 1000

Mine is the same as the previous one.

using the relation (A+B)*(A-B)=A^2- B^2

(5050+4950)x(5050-4950) 10000x100 = 1000000. root(1000000)=1000

(5050+495x(5050-4950) 10000x100 = 1000000. root(1000000)=1000

sqrt(5050^2-4950^2)=sqrt[5050^2-(5050-100)^2] =sqrt(5050^2-5050^2+200(5050)-100^2) =sqrt[(100)(2(5050)-100))] =sqrt[100(10000)]=1000

root(a^2+b^2) →root((a+b)(a-b)) let, a=5050 and b=4950. so, ans: 1000.

5050^{2} - 4950^{2} = \sqrt{1000000} 1000 answer

1) Multiply ( 5050×5050)=25502500 (4950×4950)=24502500)

2) subtracts (25502500-24502500) 1000000

3) square root : √1000000= 1000