what is the square root of 75?

Answer 1

√(75) = √(25*3) = √(25)√(3) = 5√3

Answer 2

What you do to find the square root of 75 is first see if it is rational (75 would have to be a perfect square). We know that 8²=64, and we know that 9²=81, therefore, 75 isn't a perfect square. So, it must be irrational. Therefore, we simplify √75.
What you do is you use the simplification rule for square roots, which is using products of prime factors, starting with the smallest prime factor you can do, and then increasing the prime number to the next highest prime number if you have to. But, since this is a square root, we have to use square roots of prime factors.
We see that 2 can't go into 75 evenly, so we don't use 2. We see that 3 can 25 times, so our first factor is √3. Then, since 25 is the result of 75 divided by 3, we see if 3 can go into 25 evenly, and it can't, so we go up to 5, and five can go into 25 evenly, so we divide 25 by 5, getting 5. Five can't be divided by any prime number evenly, so that √5 is our last factor. Therefore we have:

√3*√5*√5=√75

Knowing that (√x)²=x, we know that (√5)²=5. So, in our multiplication above, we have 5*√3, written simplified as 5√3.
We can check to see if the answer is right by knowing that √25=5. So, we can turn 5 in 5√3 into √25, having √25√3. Knowing that √x√y=√xy, we know √25√3=√25*3, which is √75. Therefore, simplified, √75 is 5√3. So, the answer is 5√3.
There you go. I'm glad I could help. :)

Answer 3

5

Answer 4

There is a very complicated method of finding square roots:
click start
click run
type calc
type 75
click sqrt button.

The answer is 8.66025

Answer 5

sqrt(75) = sqrt(25*3) = sqrt(25)*sqrt(3) = 5*sqrt(3).

This is approximately equal to 8.66.

Answer 6

The answer is precisely
8.6602540378443864676372317075294
it can be done in a method called long division if you want an example just mail me

Answer 7

it is 8.660254038....

or

5 square roots of 3

Answer 8

sqrt (75) = + or - 8.660254038

Answer 9

8.66

Answer 10

8.66