Question

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Answer 1

in cube root the term will be out of the root if there are three in pair and they should be in multiplication and there should not be any addition and subtraction sign in between

I have just done that only I have split a⁴ into four times a and b⁴ in four time b and taken pair of 3 a and b out of the root . and taken common from them at the last . You will understand all this language I have written here , if you know basics . or clear your basics first . .

hope this will be helpul to you

Answer 2

Given :-

$\quad \leadsto \quad \sf \sqrt[3]{a⁴b} + \sqrt[3]{ab⁴}$

To Find :-

Choose the correct option from the given

Solution :-

Consider ;

$\quad \leadsto \quad \sf \sqrt[3]{a⁴b} + \sqrt[3]{ab⁴}$

Can be written as ;

${ : \implies \quad \sf \sqrt[3]{a \times a \times a \times a \times b} + \sqrt[3]{a \times b \times b \times b \times b}}$

${ : \implies \quad \sf \sqrt[3]{\underbrace{a \times a \times a} \times a \times b} + \sqrt[3]{a \times \underbrace{b \times b \times b} \times b}}$

Now , can be written as ;

${ : \implies \quad \sf a \cdot \sqrt[3]{ab} + b \cdot \sqrt[3]{ab}}$

Take " $\bf \sqrt[3]{ab}$ " common ;

${ : \implies \quad \sf \sqrt[3]{ab} \: ( a + b ) }$

${ : \implies \quad \bf \therefore \quad \sqrt[3]{a⁴b} + \sqrt[3]{ab⁴} = ( a + b ) \: \sqrt[3]{ab}}$

Henceforth , Option B) $\bf (a+b) \: \sqrt[3]{ab}$ is correct :)