I am looking to simplify this radical/surd a model/method for future use would be appreciated 5√78×√52 I am hoping to put together a lot of basic questions as models to help people many thanks in advance
$\displaystyle \sqrt{78}\times\sqrt{52}$
Factorise the values into their smallest terms
$\displaystyle 78=2\times 3\times 13, 52= 2\times 2\times 13$
put them back under the square root in the factorised form
$\displaystyle \sqrt{2\times 3\times 13}\times\sqrt{2\times 2\times 13}$
You can bring the two square roots together
$\displaystyle \sqrt{2\times 3\times 13\times 2\times 2\times 13}$
Bring like factors together
$\displaystyle \sqrt{2^3\times 3\times 13^2}$
Remember the rules for manipulating square roots
$\displaystyle \sqrt{2^3}\times \sqrt{3}\times \sqrt{13^2}$
The square root sign goes away if something is squared
$\displaystyle 2\sqrt{2}\times \sqrt{3}\times 13$
And bring it back to one square root
$\displaystyle 26\sqrt{6}$