To determine the order of the surd [tex]\( 3 \sqrt[4]{7} \)[/tex], we need to understand what the order of a surd means. The order of a surd refers to the index of the root in the expression.
In general, a surd is written in the form [tex]\( a \sqrt[n]{b} \)[/tex], where:
- [tex]\( a \)[/tex] is the coefficient,
- [tex]\( b \)[/tex] is the radicand,
- and [tex]\( n \)[/tex] is the order of the surd.
In the given surd [tex]\( 3 \sqrt[4]{7} \)[/tex]:
- The coefficient is [tex]\( 3 \)[/tex],
- The radicand is [tex]\( 7 \)[/tex],
- The index or order of the surd is [tex]\( 4 \)[/tex].
Therefore, the order of the surd [tex]\( 3 \sqrt[4]{7} \)[/tex] is [tex]\( 4 \)[/tex].
Thus, the answer is
(d) 4
