Question

find the product of (2 root 15+root 5)(root 15+3 root 5) and the write the rational and irrational parts of the product.

Plss answer fast

Answer 1

SOLUTION

TO DETERMINE

The product :

$\sf{(2 \sqrt{15} + \sqrt{5} )( \sqrt{15} + 3 \sqrt{5} )}$

Also to write the rational and irrational parts of the product.

EVALUATION

$\sf{(2 \sqrt{15} + \sqrt{5} )( \sqrt{15} + 3 \sqrt{5} )}$

$\sf{ = \sqrt{5} \times \sqrt{5} \times (2 \sqrt{3} + 1 )( \sqrt{3} + 3 )}$

$\sf{ = 5 \times (2 \sqrt{3} + 1 )( \sqrt{3} + 3 )}$

$\sf{ = 5 \times (6 + 6 \sqrt{3} + \sqrt{3} + 3 )}$

$\sf{ = 5 ( 9 + 7 \sqrt{3} )}$

$\sf{ = 45 + 35 \sqrt{3} }$

Hence

Rational part = 45

$\sf{Irrational \: part = 35 \sqrt{3} }$

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