How do you rationalize the denominator and simplify $sqrt (1 / 3)$ ?

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Answer 1 · 2018-04-09T15:37:20

$(sqrt3)/3$

law of surds:

$(sqrta)/(sqrtb) = sqrt(a/b)$

here, $sqrt(a/b) = sqrt(1/3)$ .

using this law, $sqrt(1/3)$ is the same as $(sqrt1)/(sqrt3)$ .

$sqrt1$ is $1$ , so $sqrt(1/3)$ is the same as $1/(sqrt3)$ .

the denominator can be rationalised by multiplying both the numerator and the denominator by $sqrt3$ .

$1 * sqrt3 = sqrt3$

$sqrt3 * sqrt3 = 3$

$1/(sqrt3) = (1 * sqrt3)/(sqrt3 * sqrt3)$

$= (sqrt3)/3$

How do you rationalize the denominator and simplify sqrt (1 / 3)sqrt (1 / 3)?