1.

If √3= 1.732 then find the value of √2-√3/√2+√3 is ​

Answer»

1.04 (Approx)

Step-by-step explanation:

Given:

√3 = 1.732

√2 = 1.414 (I know)

To FIND:

The value of \dfrac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2} + \sqrt{3} }

Solution:

1st We just NEED to rationalize the denominator of question.

2nd Substituting the value of given, We will GET the answer.

Sound so simple ^_^

\frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2} + \sqrt{3} } \\ \\ \frac{( \sqrt{2} - \sqrt{3})( \sqrt{2} - \sqrt{3} ) }{( \sqrt{2} + \sqrt{3})( \sqrt{2} - \sqrt{3} ) } \\ \\ \frac{ {( \sqrt{2} - \sqrt{3} )}^{2} }{ { (\sqrt{2}) }^{2} - {( \sqrt{3} )}^{2} } \\ \\ \frac{ {( \sqrt{2}) }^{2} + {( \sqrt{3} )}^{2} - 2. \sqrt{2} . \sqrt{3} }{2 - 3} \\ \\ \frac{2 + 3 - 2 \sqrt{6} }{ - 1} \\ \\ \frac{5 - 2 \sqrt{6} }{ - 1} \\ \\ - (5 - 2 \sqrt{6} ) \\ \\ 2 \sqrt{2}. \sqrt{3} - 5

[Substituting the given VALUES ]

2 \times 1.141 \times 1.732 - 5 \\ \\ 2 \times 1.976212 - 5 \\ \\ 2 \times 1.98 - 5 \\ \\ 3.96 - 5 \\ \\ 1.04 \: \: \: [\text{approx}]

Therefore, the required answer is 1.04 approx.


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