Question

simplify
$\frac{ \sqrt[2]{10} + \sqrt[3]{10} } { \sqrt[5]{2} }$
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Answer 1

$\huge{\texttt{\underline{\underline{SOLUTION:-}}}}$

$\frac{2 \sqrt{10} + 3 \sqrt{10} }{5 \sqrt{2} }$

$\frac{5 \sqrt{10} }{5 \sqrt{2} }$

$\sqrt{5}$

Alternatively it can be written as

$2.23607$

$\huge{\texttt{\underline{STEPS:-}}}$

1) Collect the like terms

2) Reduce the fraction with 5

3) Simplify the expression

Answer 2

Hi
Here is your answer ⤵

as we know that under rood means x ½

so
$\frac{ \sqrt[2]{10} + \sqrt[3]{10} }{ \sqrt[5]{2} } = \frac{ {10}^{2 \times \frac{1}{2} } + {10}^{3 \times \frac{1}{2} } }{ {2}^{5 \times \frac{1}{2} } }$
$\frac{10 + {10}^{ \frac{3}{2} } }{ {2}^{ \frac{5}{2} } }$
as when bases are same then powers are added so.....

$\frac{ {10}^{1 + \frac{3}{2} } }{ {2}^{ \frac{5}{2} } }$
$\frac{ {10}^{ \frac{2 + 3}{2} } }{ {2}^{ \frac{5}{2} } } = \frac{ {10}^{ \frac{5}{2} } }{ {2}^{ \frac{5}{2} } }$
as we know that when powers are same bases are multiplied or divided...
$( { \frac{10}{2} })^{ \frac{5}{2} }$
now by dividing them....
${5}^{ \frac{5}{2} }$
so this is the answer

And it can be ALSO written as.....➡
$\sqrt[5]{5}$
Hope this helps u.........❤