The same operations that apply to numeric radicals can also be applied to algebraic radical expressions.

We can add or subtract **like radicals** (radicals with the same index and **radicand**) by adding the coefficients and keeping the radicand the same.

a\sqrt[n]{x}+b\sqrt[n]{x}=\left(a+b\right)\sqrt[n]{x}

\text{or}

a\sqrt[n]{x}-b\sqrt[n]{x}=\left(a-b\right)\sqrt[n]{x}

If there are no like radicals, check to see if any of the radicals can be simplified first.

Assuming y>0, simplify 10\sqrt{2y}+14\sqrt{2y}

Worked Solution

Simplify \sqrt[3]{125y}+\sqrt[3]{8y}

Worked Solution

Simplify \sqrt[3]{512v}-5\sqrt[3]{v}

Worked Solution

Simplify 6\sqrt[5]{7a}+7\sqrt[5]{5a}-3\sqrt[5]{7a}+8\sqrt[5]{5a}

Worked Solution

Idea summary

When adding and subtracting algebraic radicals, they must have the same radicand before we can add or subtract **like radicals**.

a\sqrt[n]{x}+b\sqrt[n]{x}=\left(a+b\right)\sqrt[n]{x}

\text{or}

a\sqrt[n]{x}-b\sqrt[n]{x}=\left(a-b\right)\sqrt[n]{x}