What is the square root of 1/2?

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Answer 1 · 2018-06-01T15:11:17

See a solution process below:

Square root of $1/2 = sqrt(1/2)$

We can use this rule for radicals to rewrite the expression:

$sqrt(color(red)(a)/color(blue)(b)) = sqrt(color(red)(a))/sqrt(color(blue)(b))$

$sqrt(color(red)(1)/color(blue)(2)) => sqrt(color(red)(1))/sqrt(color(blue)(2)) => 1/sqrt(2)$

Now, we can rationalize the denominator, or, in other words, remove the radical from the denominator, by multiplying by the appropriate form of $1$ :

$sqrt(2)/sqrt(2) xx 1/sqrt(2) =>$

$(sqrt(2) xx 1)/(sqrt(2) xx sqrt(2)) =>$

$sqrt(2)/((sqrt(2))^2) =>$

$sqrt(2)/2$

If, a decimal number is needed:

$sqrt(2)/2 ~= 1.4142/2 ~= 0.7071$