Answer:
The given equation is expansion of (a-b)² = a²-2ab+b²
[tex]\sqrt{81-18\sqrt{7}+7} \\ \sqrt{ {9}^{2} -2 \times 9 \times \sqrt{7}+ { \sqrt{7} }^{2} } \\ \sqrt{ {(9 - \sqrt{7})}^{2} } \\ {(9 - \sqrt{7})}[/tex]
hope that help.
Answer:
[tex]9-\sqrt{7}[/tex]
Step-by-step explanation:
Given expression: [tex]\sqrt{81-18\sqrt{7}+7}[/tex]
To simplify the given expression, use the "A minus B Whole Square" identity.
A minus B Whole Square identity
[tex](a-b)^2=a^2-2ab+b^2[/tex]
Comparing [tex]81-18\sqrt{7}+7[/tex] to the right side of the identity:
Therefore:
[tex](9-\sqrt{7})^2=81-18\sqrt{7}+7[/tex]
Finally:
[tex]\sqrt{81-18\sqrt{7}+7}=\sqrt{(9-\sqrt{7})^2}=9-\sqrt{7}[/tex]
