Simplify the square root of the polynomial using factorisation method: $\frac{a^{3} - b^{3}}{a - b}$

\sqrt{a^{2} - a b + b^{2}}

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\sqrt{a^{2} + b^{2}}

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\sqrt{a^{2} + a b + b^{2}}

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\sqrt{a + a b + b^{2}}

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Solution

The correct option is C $\sqrt{a^{2} + a b + b^{2}}$
$\sqrt{\frac{a^{3} - b^{3}}{a - b}}$
We know $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
$\sqrt{\frac{a^{3} - b^{3}}{a - b}} = \sqrt{\frac{(a - b) (a^{2} + a b + b^{2})}{a - b}}$
$=$ $\sqrt{\frac{(a - b) (a^{2} + a b + b^{2})}{a - b}}$
$=$ $\sqrt{a^{2} + a b + b^{2}}$

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Similar questions

\frac{a^{2}}{a^{2} - b^{2}} + \frac{b^{2}}{b^{2} - a^{2}}

a - a^{3} + b^{3} - b

(a^{2} - b^{2}) (a^{2} + a b + b^{2}) - a^{3} + b^{3}

(\frac{a^{3} - b^{3}}{a^{2} + b^{2} + a b})

\frac{a^{2} - b^{2}}{a - b} - \frac{a^{3} - b^{3}}{a^{2} - b^{2}}

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