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
Explanation:
Step1: Recall the definition of like radicals
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).
Step2: Analyze each option
- For the option (4(\sqrt[3]{7x})), the index is (3) and the radicand is (7x), same as the given radical (\sqrt[3]{7x}).
- For the option (\sqrt{7x}), the index is (2) (since (\sqrt{7x}=\sqrt[2]{7x})), which is different from the index (3) of (\sqrt[3]{7x}).
- For the option (x(\sqrt[3]{7})), the radicand is (7) while the radicand of (\sqrt[3]{7x}) is (7x).
- For the option (7\sqrt{x}=7\sqrt[2]{x}), the index is (2) and the radicand is (x), both different from (\sqrt[3]{7x}).
Answer:
(4(\sqrt[3]{7x}))