Answer:
[tex] \sqrt{7x} - 49[/tex]
Step-by-step explanation:
The surd to be simplified is
[tex] \sqrt{7}( \sqrt{x} - 7 \sqrt{7})[/tex]
Using the distributive property of multiplication over subtration,we obtain
[tex] = \sqrt{7} \times \sqrt{x} - \sqrt{7} \times 7\sqrt{7} [/tex]
Properties of surds state that
[tex] \sqrt{a} \times \sqrt{b} = \sqrt{ab} [/tex]
and
[tex] \sqrt{a} \times \sqrt{a} = a[/tex]
Therefore,
[tex]\sqrt{7} \times \sqrt{x} - \sqrt{7} \times 7\sqrt{7} = \sqrt{7x} - 7(7) = \sqrt{7x} - 49[/tex]
