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

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- Apr 18th 2013, 04:14 AMunklesurd/radical simplification
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

- Apr 18th 2013, 04:22 AMPlatoRe: surd/radical simplification
- Apr 18th 2013, 04:42 AMunkleRe: 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

- Apr 18th 2013, 11:34 AMShakarriRe: surd/radical simplification
$\displaystyle \sqrt{78}\times\sqrt{52}$

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

$\displaystyle 26\sqrt{6}$