## Adding, Subtracting, Dividing or Multiplying Irrational Numbers to Obtain Rational Numbers

We can find irrational numbers that add, times, divide or multiply to give rational numbers.
$2+ \sqrt{5}$
and
$2- \sqrt{5}$
add to give a rational number.
$(2 + \sqrt{5}) + (2 - \sqrt{5}) = 4$

Note that the
${} + \sqrt{5}$
cancels the
$- \sqrt{5}$
.
$\sqrt{5}$
and
$2 \sqrt{5}$
multiply to give a rational number.
$\sqrt{5}+ \times 2 \sqrt{5} =2 \times \sqrt{25} = 2 \times 5 = 10$

$\sqrt{5}$
and
$2 \sqrt{5}$
divide to give a rational number.
$\frac{\sqrt{5}}{ 2 \sqrt{5}} =\frac{1}{2}$

$3+ \sqrt{5}$
andhj
$2 + \sqrt{5}$
subtract to give a rational number.
$(3 + \sqrt{5}) - (2 + \sqrt{5}) =3 + \sqrt{5} - 2 - \sqrt{5} =1$

Note that the
${} + \sqrt{5}$
cancels the
${}+ \sqrt{5}$
.

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