We want to simplify the following expression
[tex]\sqrt{7x}(\sqrt{x}+7\sqrt{7})[/tex]
First, we can apply the distributive rule to rewrite this product
[tex]\sqrt{7x}(\sqrt{x}+7\sqrt{7})=(\sqrt{7x})(\sqrt{x})+(\sqrt{7x})(7\sqrt{7})[/tex]
Then, using the following property
[tex]\sqrt{x}\cdot\sqrt{y}=\sqrt{x\cdot y}[/tex]
we can rewrite our expression as
[tex](\sqrt{7x})(\sqrt{x})+(\sqrt{7x})(7\sqrt{7})=\sqrt{7x\cdot x}+7\sqrt{7x\cdot7}[/tex]
We can remove the squared terms out of the root
[tex]\sqrt{7x\cdot x}+7\sqrt{7x\cdot7}=x\sqrt{7}+7\cdot7\sqrt{x}=x\sqrt{7}+49\sqrt{x}[/tex]
and this is our answer.
[tex]\sqrt{7x}(\sqrt{x}+7\sqrt{7})=x\sqrt{7}+49\sqrt{x}[/tex]
