What is square root of 2/3?

Question

Step by step thanks.

Answer 1

LEARN PEDMAS !!  The sqrt of 2 is 1.4142 ... AND THEN divide by 3 = .4714.  Others answered "What is sqrt (2/3) !!  Computers care !!

Answer 2

Any calculator can give you an approximation: 0.81649658092772603273242802490196

If you want to do it manually:

Guess a number that's halfway between 2/3 and 1, which is 5/6.

2/3 divided by 5/6 is 4/5. So the final answer is somewhere between 4/5 and 5/6.

Guess a number that's halfway between 4/5 and 5/6, which is 49/60.

2/3 divided by 49/60 is 120/147. So the final answer is somewhere between 120/147 and 49/60.

Guess a number that's halfway between 120/147 and 49/60...

By the above method, each guess will get closer and closer to the correct answer. It'll never be exact, but it'll eventually get so close that the difference will be negligible.

Answer 3

√(2/3)

The root of a quotient is the same as the quotient of the roots, so:

√(2) / √(3)

Now to rationalize the denominator, multiply both halves by √3:

√(2) √(3) / [√(3) √(3)]

Reversing step 1, the product of two roots is the same as the root of the product, so:

√(6) / √(9)

And since √9 simplifies to a rational value:

√(6) / 3

or:

(1/3)√6