Simplifying Radical Expressions: Videos & Practice Problems

Which statement best captures the product rule for n^th roots?

Which formula expresses the quotient rule for radicals of index $n$?

Condense the product $\sqrt{3}\cdot \sqrt{11}$.

Compute $\sqrt{2}\cdot \sqrt{18}$ and give the final simplified numerical answer.

Expand and fully simplify $\sqrt{80}$ into a product of an integer and a radical.

Simplify $\sqrt{\frac{144}{25}}$ by applying the quotient rule.

Simplify $\frac{\sqrt{300}}{\sqrt{3}}$ fully using the quotient rule.

Simplify $\sqrt{18x^3}$ by factoring the radicand to extract perfect squares, given $x\ge 0$.

Simplify the expression $\sqrt{x^5}$, assuming $x\ge 0$.

Rationalize the denominator and simplify $\frac{3}{\sqrt{2}}$.

Rationalize the denominator and simplify: $\frac{5}{\sqrt[3]{2}}$

You must simplify $\sqrt{\frac{x^{2}y}{x}}$. Which sequence of steps will always lead to the simplest exact result, assuming $x>0$ and $y\ge 0$?

Compute $\sqrt[3]{9}\cdot \sqrt[3]{3}$.

Simplify the product $\sqrt[4]{8}\cdot \sqrt[4]{2}$.

Simplify $\sqrt{\frac{50x^7}{2x^2}}$.

Which of the following radicals is fully simplified?

Is the expression $\sqrt{33}$ fully simplified? Choose the best justification.

Select the statement that accurately lists all the conditions required for a radical to be considered fully simplified (assuming principal roots and nonnegative variables).

Evaluate $\sqrt[7]{128}$ and simplify the result.

Simplify the sum $\sqrt{18}+\sqrt{8}$.

A rectangular garden has side lengths of $\sqrt{50}$ meters and $\sqrt{2}$ meters. Compute and simplify the area.

You need to simplify ∛((54 x⁷) / x). Which of these sequences of steps produces a correct fully simplified form?

Which of the following is the correct factorization step to begin simplifying $\sqrt{72}$?