Question

simply the following



$\sqrt{4 + \sqrt{4} + \sqrt{4} + \sqrt{4} \div \sqrt{5} }$
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Answer 1

$\sqrt{4 + \sqrt{4} + \sqrt{4} + \sqrt{4} \div \sqrt{5} }$

write the division as fraction

$\sqrt{4 + \sqrt{4} + \sqrt{4} + \sqrt{ \frac{4}{ \sqrt{5} } } }$

Rationalize the denominator

$\sqrt{4 + \sqrt{4} + \sqrt{4} + \sqrt{ \frac{4 \sqrt{5} }{5} } }$

to take a root of fraction take the the root of the number and denominator separately

$\sqrt{4 + \sqrt{4} + \sqrt{4} + \frac{ \sqrt{4 \sqrt{5} } }{ \sqrt{5} } }$

Simplify the redical expression

$\sqrt{4 + \sqrt{4} + \sqrt{4} + \frac{2 \sqrt{ \sqrt{5} } }{5} }$

$\bold{using \sqrt{m \sqrt{n \sqrt{a} } } } = \sqrt[mn]{a}$Simply the expression

$\sqrt{4 + \sqrt{4} + \sqrt{4} + \frac{ 2\sqrt[4]{5} }{ \sqrt{5} } }$

rationalize the denominator

$\sqrt{4 + \sqrt{4} + \sqrt{4} + \frac{2 \sqrt[4]{5} \sqrt{5} }{5} }$

$\bold{using \: \sqrt[n]{a} = \sqrt[mn]{ {a}^{m} } }$expand the expression

$\sqrt{4 + \sqrt{4} + \sqrt{4} + \frac{2 \sqrt[4]{5}{ \sqrt[4]{ {5}^{2} } } }{5} }$

the product of roots with the same index is equal to the root of the product

$\sqrt{4 + \sqrt{4} + \sqrt{4} + \frac{2 \sqrt[4]{5 \times {5}^{2} } } {5} }$

calculate the product

$\sqrt{4 + \sqrt{4} + \sqrt{4} + \frac{2 \sqrt[4]{ {5}^{3} } }{5} }$

evalute the power

$\sqrt{4 + \sqrt{4} + \sqrt{4} + \frac{2 \sqrt[4]{125} }{5} }$

Alternate form

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