Question

rationalize the denominator and simplify to find the value of
4/√5+√3​

Answer 1

Step-by-step explanation:

By rationalizing the denominator:

4/√5+√3 *√5-√3/√5-√3

⇒4(√5-√3) / (√5)²-(√3)²

⇒4√5-4√3 / 5-3

⇒4√5 -4√3 / 2

⇒4(√5-√3) / 2

since 4 is divisible by 2.

so,

⇒2(√5-√3)

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Answer 2

The value $\dfrac{4 }{\sqrt{5}+\sqrt{3}}$ is equal to $2(\sqrt{5}-\sqrt{3})$.

Step-by-step explanation:

We have,

$\dfrac{4 }{\sqrt{5}+\sqrt{3}}$

To find, the value $\dfrac{4 }{\sqrt{5}+\sqrt{3}}$ = ?

∴ $\dfrac{4 }{\sqrt{5}+\sqrt{3}}$

The rationalize the denominator, we get

$=\dfrac{4 }{\sqrt{5}+\sqrt{3}}\times \dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{5}-\sqrt{3}}$

Using the algebraic identity,

$a^{2} -b^{2} =(a+b)(a-b)$

$=\dfrac{4(\sqrt{5}-\sqrt{3}) }{\sqrt{5}^2-\sqrt{3}^2}$

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

$=\dfrac{4(\sqrt{5}-\sqrt{3}) }{2}$

$=2(\sqrt{5}-\sqrt{3})$

Thus, the value $\dfrac{4 }{\sqrt{5}+\sqrt{3}}$ is equal to $2(\sqrt{5}-\sqrt{3})$.