Question

On rationalizing the denominator of √5 - √3 / √5 + √3 we get​

Answer 1

Question:

• To rationalize the denominator?

Answer:

Step 1:

⟿$\green{ \dfrac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } }$

Step 2:

⟿$\green{\dfrac{( \sqrt{5} - \sqrt{3}) \times( \sqrt{5} - \sqrt{3} ) }{ (\sqrt{5} + \sqrt{3})( \sqrt{5} - \sqrt{3} ) }}$

Step 3:

⟿$\green{ \dfrac{{( \sqrt{5} - \sqrt{3}) }^{2} }{( \sqrt{5} \times \sqrt{5} ) - ( \sqrt{3} \times \sqrt{3} )}}$

Step 4:

⟿$\green{\dfrac{5 + 3 - 2 \times \sqrt{5} \times \sqrt{3} }{5 - 3}}$

Step 5:

⟿$\green{ \dfrac{8 - 2 \sqrt{15} }{2}}$

Step 6:

⟿$\green{2( \dfrac{4 - \sqrt{15} }{2} )}$

Step 7:

⟿$\blue{4 - \sqrt{15} ✓}$

Explanation:

To rationalize the denominator we have to multiply it with same same number but by changing the signs

• eg:(√3-√2)×(√3+√2)
• =(√3)²-(√2)²
• =3-2
• =1

↑The same rule is applied above

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Answer 2

Step-by-step explanation:

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