( 2 + √(3))( 3 + √(5)) = 2( 3 + √(5)) + √(3)( 3 + √(5)) = 6 + 2√(5) #160; + 3√(3) #160; + √(15) = 6 + 3√(3) #160; + 2√(5) #160; + √( ...

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Multiplication of Surds

2+√33+√5=?

Question

$(2 + \sqrt{3}) (3 + \sqrt{5}) =$ ?

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Solution

$(2 + \sqrt{3}) (3 + \sqrt{5})$
$= 2 (3 + \sqrt{5}) + \sqrt{3} (3 + \sqrt{5})$
$= 6 + 2 \sqrt{5} + 3 \sqrt{3} + \sqrt{15}$
$= 6 + 3 \sqrt{3} + 2 \sqrt{5} + \sqrt{15}$ , which is the required value.

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