Question

(1−√(5))×(2−√(5))
$(1 + 4 \sqrt{10} )(2 - \sqrt{10} )$

Answer 1

To simplify these expressions, you can either use a calculator (which I'm assuming your teacher doesn't want you to do) or FOIL (distribute).

The first one would be:

$(1- \sqrt{5}) (2- \sqrt{5}) \newline =(1)(2)+(1)(- \sqrt{5} )+(- \sqrt{5})(2)+(- \sqrt{5})(- \sqrt{5}) \newline =2- \sqrt{5}-2 \sqrt{5}+5 \newline =7-3 \sqrt{5}$

The second one would be:

$(1+4 \sqrt{10})( 2- \sqrt{10}) \newline =(1)(2)+(1)(- \sqrt{10})+(4 \sqrt{10} )(2) +(4 \sqrt{10})(- \sqrt{10}) \newline =2-\sqrt{10}+8 \sqrt{10} -40 \newline =-38+7 \sqrt{10}$