Question

Simplify (√3-√2) (√3+√2). Use this to compute 1/√3-√2and1/√3+√2correct to two decimal places

Answer 1

$( {x}^{2} - y {}^{2} ) = (x - y)(x + y)$

$(\sqrt{3} - \sqrt{2} )( \sqrt{3 } + \sqrt{2}) = ( \sqrt{ {3}^{} }) {}^{2} - ( \sqrt{2} ) {}^{2}$

$3 - 2 = 1$

$\frac{1}{ \sqrt{3} - \sqrt{2} } = \frac{( \sqrt{3} - \sqrt{2} )( \sqrt{3 } + \sqrt{2}) }{( \sqrt{3} - \sqrt{2} )}$

$= \sqrt{3} + \sqrt{2}$

$1.732 + 1.414 = 3.146 = 3.15$

$\frac{1}{ \sqrt{3} + \sqrt{2} } =$

$= 1.732 - 1414 = 0.318 = 0.32$