Question
Simplify the expression: (5 + $\sqrt{5}$)(5 - $\sqrt{5}$)
✓
Answer
$(5-\sqrt{5})(5+\sqrt{5})$
According to the formula $a^2-b^2=(a+b)(a-b)=(5)^2-(\sqrt{5})^2$
So we get
$=25-5$
$=20$
Hence $(5-\sqrt{5})(5+\sqrt{5})$ is rational.
According to the formula $a^2-b^2=(a+b)(a-b)=(5)^2-(\sqrt{5})^2$
So we get
$=25-5$
$=20$
Hence $(5-\sqrt{5})(5+\sqrt{5})$ is rational.
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