Question

what is the simplified form of square root 98n^19
A. 2n^9 square root 7
B. 7n^4 square root 2n^3
C. 7n^9 square root 2n
D. 4n^9 square root 6n

Answer 1

We have
\[\large \sqrt{98n^{19}}\]
Factors of 98
\[98= 1\times 2 \times 7 \times 7\]
also
\[n^{19}= n^9 \times n^9 \times n\]
so
\[\large \sqrt{ 2 \times 7 \times 7\times n^9 \times n^9 \times n}\]
So we have
\[ 7\times n^9 \sqrt{2 \times n}\]
or
\[\large 7n^9 \sqrt{2n}\]