Math, asked by pallavipallu1106, 7 months ago

rationalize the denominator and simplify 14/5√3-√5​

Answers

Answered by vivekmane123
0

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

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