Question

What is the square root of 35000 ​

Answer 1

`50√(14)`

Explanation:

`√(35000 ​)\\ \\\mathrm{Prime\:factorization\:of\:}35000:\quad 2^3*\:5^4*\:7\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^(b+c)=a^b*\:a^c\\\\2^3*\:5^4*\:7=2^2*\:2*\:5^4*\:7\\\\=√(2^2*\:5^4*\:2*\:7)\\\\\mathrm{Apply\:radical\:rule}:\quad √(ab)=√(a)√(b)\\\\√(2^2*\:5^4*\:2*\:7)=√(2^2)√(5^4)√(2*\:7)\\\\√(2^2)=2\\\\=2√(5^4)√(2*\:7)\\\\√(5^4)=25`

`=2*\:25√(2*\:7)\\\\2*\:25√(2*\:7)=50√(14)`

Answer 2

187 is closer so the square root of 35000 would be 187.082... or just

√35000

Explanation:

187 x 187 = 34960

188 x 188 = 35344

Now find which is closer

35344-35000=31844

35000-34960=40

Hope this helps :)