Question 87860
{{{sqrt(1/6)}}} Start with the given expression


{{{sqrt(1)/sqrt(6)}}}  Break up the square roots using the identity {{{sqrt(x/y)=sqrt(x)/sqrt(y)}}}

Lets simplify the numerator

Since 1 is a perfect square, we can take the square root of 1 to get a clean number

{{{sqrt(1)=1}}}


Lets simplify the denominator


{{{sqrt(6)}}} Start with the given expression
The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. This way the perfect square will become a rational number.

So let's list the factors of 6

Factors:

1, 2, 3,6

Since none of these factors are perfect squares, we cannot simplify {{{sqrt(6)}}}


So the expression

{{{sqrt(1/6)}}}

simplifies to 

{{{1/sqrt(6)}}}