Question
State whether the following number is rational or irrational:$(5-\sqrt{5})^2$
✓
Answer
$(5-\sqrt{5})^2 $
$ =(5)^2+(\sqrt{5})^2-2 \times 5 \times \sqrt{5}$
$=25+5-10 \sqrt{5}$
$=30-10 \sqrt{5},$
which is irrational.
$ =(5)^2+(\sqrt{5})^2-2 \times 5 \times \sqrt{5}$
$=25+5-10 \sqrt{5}$
$=30-10 \sqrt{5},$
which is irrational.
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