rationalize the denominator of 5√3 / √5-√2
step by step pls
Answers
Step-by-step explanation:
5√3/ √5-√2
multiply √5+√2 in numerayor and denominator
=
Answer:
Solution:
\dfrac{5}{\sqrt{3} -\sqrt{5} }
3
−
5
5
Rationalize the denominator
=\dfrac{5}{\sqrt{3} -\sqrt{5} } \times \dfrac{\sqrt{3} +\sqrt{5} }{\sqrt{3} +\sqrt{5} }=
3
−
5
5
×
3
+
5
3
+
5
apply Distributive property and use (a + b)(a - b) = a² - b²
= \dfrac{5\sqrt{3} +5\sqrt{5} }{(\sqrt{3})^2 -(\sqrt{5})^2 }=
(
3
)
2
−(
5
)
2
5
3
+5
5
(√a)² = a
= \dfrac{5\sqrt{3} +5\sqrt{5} }{3 -5 }=
3−5
5
3
+5
5
= \dfrac{5\sqrt{3} +5\sqrt{5} }{-2 }=
−2
5
3
+5
5
= -\dfrac{5\sqrt{3}}{2 }- \dfrac{ 5\sqrt{5} }{2 }=−
2
5
3
−
2
5
5
= -\dfrac{5 }{2 }\left( \sqrt{3} + \sqrt{5}\right)=−
2
5
(
3
+
5
)
\dfrac{5}{\sqrt{3} -\sqrt{5} }
3
−
5
5
= -\dfrac{5 }{2 }\left( \sqrt{3} + \sqrt{5}\right)=−
2
5
(
3
+
5
)