Please help me figure out the relationship

[poodles]

This must be a gap in my knowledge but how does 1/sqrt10 = sqrt10/10

 

[Harry_the_cat]

\(\displaystyle \frac{1}{\sqrt{10}}= \frac{1}{\sqrt{10}} * \frac{\sqrt{10}}{\sqrt{10}} = \frac{\sqrt{10}}{10}\).

This process is called "rationalising the denominator".

 

[Deleted member 4993]

This must be a gap in my knowledge but how does 1/sqrt10 = sqrt10/10

You know:

sqrt(10) * sqrt(10) = 10 ............................. Now divide both sides by 10

{sqrt(10) * sqrt(10)} / 10 = 1 .. ................... Now divide both sides by sqrt(10)

sqrt(10) / 10 = 1 / sqrt(10)

 

[Thadriel]

Use a calculator to prove to yourself they are equal (with proper use of parentheses if necessary on your calculator), and then try to figure out why. The two posts above explain it.
You could think of post #2 in the same way you might think about this:

\(\displaystyle 4= \frac{4}{1} * \frac{2}{2} = \frac{8}{2}\).
It’s kind of the same thing, except in Harry the Cat’s example, the multiplication results in making the denominator easier to read.