In finding radicals, we use addition, subtraction, division and multiplication.

When adding and subtracting, the coefficient are combined when the radicand are the same. The strategies for simplifying polynomials can be used to simplify sums and differences of radicals

For example,

√3 + 2√7 + 4√3 = √3 + 4√3 + 2 √7 = 5√3 + 2 √7

When multiplying a radical, foiling is necessary

For example,

a√b * c√d = ac√bd

When dividing a radical, conjugating is necessary

No √ in denominator.

For example, = as we multiply √3 on denominator

It is always important to simplify and removing square from radicand. It is going to make it easier to calculate.