Question

18. Find the simplified value of
√5 + √3/√5-√3
​

Answer 1

Answer:

√5 + √3/√5-√3 = 4 + √15

Step-by-step explanation:

In the given fraction, the denominator is irrational. Hence, we have to rationalize the denominator first and then simplify it.

Rationalizing factor = √5 + √3

Multiply and divide the given fraction by √5 + √3

$= \dfrac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3}} \times \dfrac{ \sqrt{5} + \sqrt{3}}{ \sqrt{5} + \sqrt{3}} \\ = \dfrac{ { (\sqrt{5} + \sqrt{3})}^{2} }{( \sqrt{5} - \sqrt{3})( \sqrt{5} + \sqrt{3})} \\ = \frac{ \sqrt{ 5}^{2} + { \sqrt{3} }^{2} + 2( \sqrt{5})( \sqrt{3} )}{ { \sqrt{5} }^{2} - { \sqrt{3} }^{2} } \\ = \dfrac{5 + 3 + 2 \sqrt{15} }{5 - 3} \\ = \dfrac{8 + 2 \sqrt{15} }{2} \\ = \frac{2(4 + \sqrt{15} )}{2} \\ = 4 + \sqrt{15}$

= 4 + 3.873

= 7.873

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Identities used :

(a + b)² = a² + b² + 2ab

(a + b) (a – b) = a² – b²

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#Know more :

★ Rationalizing factor :

⇒ The factor of multiplication by which rationalization is done, is called as rationalizing factor.

⇒ If the product of two surds is a rational number, then each surd is a rationalizing factor to other.

⇒ To find the rationalizing factor,

=> If the denominator contains 2 terms, just change the sign between the two terms.

For example, rationalizing factor of (3 + √2) is (3 - √2)

=> If the denominator contains 1 term, the radical found in the denominator is the factor.

For example, rationalizing factor of √2 is √2

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Answer 2

Answer:

4+√5

Step-by-step explanation:

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