# How do you simplify the square root of 750?

May 9, 2018

$10 \times \sqrt{7.5}$,

#### Explanation:

With modern calculators - OK, even with our old slide rules - it really can be calculated directly. BUT, if you want to simplify the expression first into smaller units, you can separate a 'square' factor from the original value.
$\sqrt{750} = \sqrt{100 \times 7.5} = \sqrt{100} \times \sqrt{7.5}$
This is now $10 \times \sqrt{7.5}$, but I'm now sure that easier the new radical is any to calculate that the original.

We could take it one more level down with 7.5 = 4 xx 1.875 to
$20 \times \sqrt{1.875}$ Again, is it getting simpler, or just more complicated?