√84 divided by 2√3

Simplify with out using a calculator the square root of 704.

factorization can be done by successive division by the prime numbers:

Now we employ the properties of square roots:



:)

How do you solve square roots of irrational numbers w/o a calculator? for example sqroot of 68.

There are many ways. One way is to sort of work backwards:
64 < 68 < 81 (close to 64),
so sqrt(68) is close to 8.
Then by trial and error, determine that
8.2 < sqrt(68) < 8.3
Continue this process as long as you are able.

The square root of 6 multiply by the square root of 6

√(49x^2+14x+1)

±√324 - how do you solve this

A method of extracting roots is to use the factorization of a number (by successively dividing out primes until the number is manageable) 
factoring 324... 
324=2*162=
2^2*81=2^2*9^2 

so that 324 = (2*9)^2 = 18^2 

therefore the square root of 324 is 18 
±√324 = ±18

:)

Square Root of a product