$2\sqrt{27}+3\sqrt{3}$ 

Simplify the above radical.

Multiply and simplify. Assume that all variables are positive.  $\sqrt{8y^5}\cdot\sqrt{40y^2}$  

Multiply and simplify. Assume that all variables are positive.

Divide and simplify. Assume that all variables are positive.  $\frac{\sqrt{180x^5}}{\sqrt{5x^3}}$   

Divide and simplify. Assume that all variables are positive.

 $\frac{\sqrt{5x^4}}{\sqrt{2x^2y^3}}$  Rationalize the denominator of the expression. Assume that all variables are positive.

 $\frac{\sqrt{12x^4y^2}}{\sqrt{5xy}}$  Rationalize the denominator of the expression. Assume that all variables are positive.

Rationalize the denominator of the expression. Assume that all variables are positive.

Rationalize the denominator of the expression. Assume that all variables are positive.

 $\sqrt{5}\left(\sqrt{5}+\sqrt{15}\right)$  Multiply and simplify. Assume that all variables are positive.

We add or subtract the indices and retain the radicand when we combine similar radicals.

The product of the square root of two positive integers is equal to the square root of the product of these integers.

The process of removing the radical from the numerator is called rationalizing the denominator.

3. In the process of multiplying radicals, there are only three cases to be considered: (a) To multiply radicals of the same order. (b) To multiply binomials involving radicals. (c) To multiply radicals of different orders.