How do you rationalize the denominator and simplify $\frac{30}{\sqrt{18}}$ $30/sqrt18$ ?

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How do you rationalize the denominator and simplify $\frac{30}{\sqrt{18}}$ $30/sqrt18$ ?

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Answer 1 · 2016-03-21T10:55:48

$5 \sqrt{2}$ $5sqrt2$

Explanation:

To rationalise the denominator multiply numerator and denominator by $\sqrt{18}$ $sqrt18$
$-------------------------------------------------------$ $"-------------------------------------------------------"$

Note : $\sqrt{a} \times \sqrt{a} = a eliminate the radical$ $sqrtaxxsqrta = a " eliminate the radical "$

example : $\sqrt{100} \times \sqrt{100} = 10 \times 10 = 100$ $sqrt100xxsqrt100 = 10xx10 = 100$

Also : $\sqrt{a} \times \sqrt{b} \Leftrightarrow \sqrt{a} b$ $sqrtaxxsqrtb hArr sqrtab$
$-----------------------------------------------------------$ $"-----------------------------------------------------------"$

$\Rightarrow \frac{30}{\sqrt{18}} \times \frac{\sqrt{18}}{\sqrt{18}} = \frac{30 \sqrt{18}}{18} = \frac{5 \sqrt{18}}{3}$ $rArr 30/sqrt18xxsqrt18/sqrt18=( 30sqrt18)/18 = (5sqrt18)/3$

now $\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3 \sqrt{2}$ $sqrt18 = sqrt(9xx2) = sqrt9xxsqrt2 = 3sqrt2$

hence : $(5sqrt18)/3 = (5xx3sqrt2)/3 = (5cancel(3)sqrt2)/cancel(3)$

$rArr 30/sqrt18 = 5sqrt2$

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How do you rationalize the denominator and simplify $\frac{30}{\sqrt{18}}$ $30/sqrt18$ ?

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How do you rationalize the denominator and simplify 30/sqrt1830√1830/sqrt18?

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How do you rationalize the denominator and simplify $\frac{30}{\sqrt{18}}$ $30/sqrt18$ ?