Simplify frac 5 sqrt 7 3 sqrt 7 - JAMB Mathematics 2009 Question
Simplify \(\frac{5+\sqrt{7}}{3+\sqrt{7}}\)
A
17-√7
B
4-√7
C
15+√7
D
7-√7
correct option: b
\(\frac{5+\sqrt{7}}{3+\sqrt{7}}=\frac{5+\sqrt{7}}{3+\sqrt{7}}\times \frac{3-\sqrt{7}}{3-\sqrt{7}}\\
=\frac{(5+\sqrt{7})(3-\sqrt{7})}{3^2 - \sqrt{7}^2}\\
=\frac{15-5\sqrt{7}+3\sqrt{7}-7}{9-7}\\
=\frac{8-2\sqrt{7}}{2}\)
Factorize then divide by 2
\(=\frac{2(4-\sqrt{7}}{2}\\ =4-\sqrt{7}\)
Factorize then divide by 2
\(=\frac{2(4-\sqrt{7}}{2}\\ =4-\sqrt{7}\)
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