Question

write all the formula of chapters rational numbers​

Answer 1

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$\huge\bf{Answer:-}$

1. For positive real numbers a and bbl, following identities hold:-

$\sqrt{ab} = \sqrt{a} \sqrt{b} \\ \sqrt{ \frac{a}{b} } = \frac{ \sqrt{a} }{ \sqrt{b} } \\ ( \sqrt{a} + \sqrt{b} )( \sqrt{a} - \sqrt{b} = a - b \\ (a + \sqrt{b} )(a - \sqrt{b} = {a}^{2} - {b}^{2} \\ ( \sqrt{a} + \sqrt{b} ) {}^{2} = a + \sqrt{ab} + b$

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2. To rationalize the denominator of

$\frac{1}{ \sqrt{a} + b }$

We multiply this by

$\frac{ \sqrt{a} - b }{ \sqrt{a} - b }$

where a and b are integers.

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3. Let a > 0 be a real number and p and q be rational numbers. Then,

${a}^{p} \times {a}^{q} = {a}^{p + q} \\ ( {a}^{p} ) {}^{q} = {a}^{pq} \\ \frac{ {a}^{p} }{ {a}^{q} } = {a}^{p - q} \\ {a}^{p} {b}^{p} = (ab) {}^{p}$

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