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

2. Re: surd/radical simplification

Originally Posted by unkle
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
FACTOR:
$78=2\cdot 3\cdot 13~\&~52=2^2\cdot 13$.

3. Re: surd/radical simplification

please could you write that as a product of an integer so I can show the working out many thanks in advance

4. Re: surd/radical simplification

$\sqrt{78}\times\sqrt{52}$

Factorise the values into their smallest terms
$78=2\times 3\times 13, 52= 2\times 2\times 13$

put them back under the square root in the factorised form
$\sqrt{2\times 3\times 13}\times\sqrt{2\times 2\times 13}$

You can bring the two square roots together
$\sqrt{2\times 3\times 13\times 2\times 2\times 13}$

Bring like factors together
$\sqrt{2^3\times 3\times 13^2}$

Remember the rules for manipulating square roots
$\sqrt{2^3}\times \sqrt{3}\times \sqrt{13^2}$

The square root sign goes away if something is squared
$2\sqrt{2}\times \sqrt{3}\times 13$

And bring it back to one square root
$26\sqrt{6}$