rationalize the denominator and simplify 14/5√3-√5
Answers
Answer:
\frac{14}{5\sqrt{3}-\sqrt{5}}
5
3
−
5
14
=\frac{5\sqrt{3}+\sqrt{5}}{5}
5
5
3
+
5
Step-by-step explanation:
Given \frac{14}{5\sqrt{3}-\sqrt{5}}
5
3
−
5
14
Multiply numerator and denominator by 5\sqrt{3}+\sqrt{5}5
3
+
5
,we get
=\frac{14(5\sqrt{3}+\sqrt{5})}{(5\sqrt{3}-\sqrt{5})(5\sqrt{3}+\sqrt{5})}
(5
3
−
5
)(5
3
+
5
)
14(5
3
+
5
)
=\frac{14(5\sqrt{3}+\sqrt{5})}{(5\sqrt{3})^{2}-(\sqrt{5})^{2}}
(5
3
)
2
−(
5
)
2
14(5
3
+
5
)
/* By algebraic identity:
(a+b)(a-b)=a²-b² */
=\frac{14(5\sqrt{3}+\sqrt{5})}{75-5}
75−5
14(5
3
+
5
)
= \frac{14(5\sqrt{3}+\sqrt{5})}{70}
70
14(5
3
+
5
)
After cancellation, we get
= \frac{5\sqrt{3}+\sqrt{5}}{5}
5
5
3
+
5
Therefore,
\frac{14}{5\sqrt{3}+\sqrt{5}}
5
3
+
5
14
= \frac{5\sqrt{3}+\sqrt{5}}{5}
5
5
3
+
5