# How do you simplify sqrt(98n^19)?

Jan 15, 2016

$= 7 \textcolor{b l u e}{{n}^{\frac{19}{2}}} \sqrt{2}$

#### Explanation:

$\sqrt{98 {n}^{19}}$

Upon prime factorising (simplification):
$98 = 7 \times 7 \times 2$

$\sqrt{98 {n}^{19}} = \sqrt{7 \times 7 \times 2 \times {n}^{19}} = \sqrt{{7}^{2} \times 2 \times {n}^{19}} = 7 \sqrt{2 \times {n}^{19}}$

Further, Square root , can also be called as second root so in terms of fraction:
sqrt(n^19)=n^(19xx 1/2) = n^color(blue)(19/2

The expression now becomes:

$7 \sqrt{2 \times {n}^{19}} = 7 \times \textcolor{b l u e}{{n}^{\frac{19}{2}}} \sqrt{2}$

$= 7 \textcolor{b l u e}{{n}^{\frac{19}{2}}} \sqrt{2}$