which of the following is a like radical to $sqrt3{7x}$?\n$4(sqrt3{7x})$\n$sqrt{7x}$\n$x(sqrt3{7})$\n$7sqrt{x…

which of the following is a like radical to $sqrt3{7x}$?\n$4(sqrt3{7x})$\n$sqrt{7x}$\n$x(sqrt3{7})$\n$7sqrt{x}$

Answer

Like radicals have the same index and the same radicand. The given radical is $\sqrt[3]{7x}$, which has an index of 3 and a radicand of $7x$.

Option 1: $4\sqrt[3]{7x}$ has an index of 3 and a radicand of $7x$, so it is a like - radical.
Option 2: $\sqrt{7x}$ has an index of 2, different from the index of 3 in $\sqrt[3]{7x}$, so it is not a like - radical.
Option 3: $x\sqrt[3]{7}$ has a radicand of 7, different from the radicand of $7x$ in $\sqrt[3]{7x}$, so it is not a like - radical.
Option 4: $7\sqrt{x}$ has an index of 2 and a radicand of $x$, different from the given radical, so it is not a like - radical.

$4\sqrt[3]{7x}$