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3 years ago

Which is the best site for online Math and English

Mathematics

2 answers:

ankoles [38]3 years ago

8 0

Answer:

I use m a t h w a y for math but i dnot know about english

Step-by-step explanation:

Kisachek [45]3 years ago

6 0

Answer:

Khan Academy, IXL, and edX

Step-by-step explanation:

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Rationalise the denominator of 5/√(3-√5) Pls send the answer by today

Maksim231197 [3]

Answer:

$\dfrac{5(3+\sqrt{5})\sqrt{3-\sqrt{5}}}{4}$

$\textsf{or}\quad \dfrac{5\sqrt{3+\sqrt{5}}}{2}$

Step-by-step explanation:

$\textsf{Given expression}:\dfrac{5}{\sqrt{3-\sqrt{5}}}$

Method 1

$\textsf{Multiply by the conjugate}\quad \dfrac{\sqrt{3-\sqrt{5}}}{\sqrt{3-\sqrt{5}}}:$

$\implies \dfrac{5}{\sqrt{3-\sqrt{5}}} \times \dfrac{\sqrt{3-\sqrt{5}}}{\sqrt{3-\sqrt{5}}}=\dfrac{5\sqrt{3-\sqrt{5}}}{(\sqrt{3-\sqrt{5}})(\sqrt{3-\sqrt{5}})}$

Simplify the denominator using the radical rule $\sqrt{a} \sqrt{a} =a$ :

$\implies (\sqrt{3-\sqrt{5}})(\sqrt{3-\sqrt{5}})=3-\sqrt{5}$

Therefore:

$\implies \dfrac{5\sqrt{3-\sqrt{5}}}{(\sqrt{3-\sqrt{5}})(\sqrt{3-\sqrt{5}})}= \dfrac{5\sqrt{3-\sqrt{5}}}{3-\sqrt{5}}$

$\textsf{Multiply by the conjugate}\quad \dfrac{3+\sqrt{5}}{3+\sqrt{5}}:$

$\implies \dfrac{5\sqrt{3-\sqrt{5}}}{3-\sqrt{5}} \times \dfrac{3+\sqrt{5}}{3+\sqrt{5}}=\dfrac{5\sqrt{3-\sqrt{5}}(3+\sqrt{5})}{(3-\sqrt{5})(3+\sqrt{5})}$

Simplify the denominator:

$\implies (3-\sqrt{5})(3+\sqrt{5})=9+3\sqrt{5}-3\sqrt{5}-5=4$

Therefore:

$\implies \dfrac{5(3+\sqrt{5})\sqrt{3-\sqrt{5}}}{4}$

Method 2

$\textsf{Multiply by the conjugate}\quad \dfrac{\sqrt{3+\sqrt{5}}}{\sqrt{3+\sqrt{5}}}:$

$\implies \dfrac{5}{\sqrt{3-\sqrt{5}}} \times \dfrac{\sqrt{3+\sqrt{5}}}{\sqrt{3+\sqrt{5}}}=\dfrac{5\sqrt{3+\sqrt{5}}}{(\sqrt{3-\sqrt{5}})(\sqrt{3+\sqrt{5}})}$