# What is square root of 2/3?

Step by step thanks.

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

• 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.

• √(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