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Find an example of two irrational numbers
a and
b for which
a!=b and
(a)/(b) is rational.

$16$ . Find an example of two irrational numbers $a$ and $b$ for which $a \neq b$ and $\frac{a}{b}$ is rational.

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Write a quadratic function from its x-intercepts and another point

Full solution

Q.

16

. Find an example of two irrational numbers

a

and

b

for which

a \neq b

and

\frac{a}{b}

is rational.

Choose $\sqrt{2}$ as a: Let's pick the square root of $2$ ( $\sqrt{2}$ ) as our first irrational number, $a$ . We know that $\sqrt{2}$ is irrational.
Select $2\sqrt{2}$ as $b$ : Now, let's choose $2\sqrt{2}$ as our second irrational number, $b$ . Since $2$ is a rational number and the square root of $2$ is irrational, their product is also irrational.
Calculate ratio $a/b$ : Now, we calculate the ratio $a/b$ which is $(\sqrt{2})/(2\sqrt{2})$ . We simplify this by dividing $\sqrt{2}$ by $2\sqrt{2}$ .
Simplify the ratio: The ratio simplifies to $(\sqrt{2})/(2\sqrt{2}) = \frac{1}{2}$ after canceling out the $\sqrt{2}$ in the numerator and denominator.
Final result: Since $\frac{1}{2}$ is a rational number, we have found two irrational numbers $a$ and $b$ , where $a \neq b$ , and their ratio $\frac{a}{b}$ is rational.

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