How do you simplify radical expressions?

Question

examples :

√80

5√18

√32+√50

(5√3)²

can you please tell me how to simplify them? i have about 25 questions on it for summer homework but i dont know how to do the problems

Answer 1

√80 (find the largest perfect square factor of 80, which is 16)

√16 * √5 (take the square root of 16)

4√5 <===

5√18 (again, find the largest perfect square factor of 18, which is 9)

5*√9 * √2 (take the square root of 9)

5*3√2 (multiply)

15√2 <===

√32 + √50

√16*√2 + √25*√2

4√2 + 5√2 (add coefficients)

9√2 <===

(5√3)^2

5√3 * 5√3 (multiply the coefficients together and the square roots together)

5*5√(3*3)

25*3

75 <===

Remember that a square root multiplied by the same square root gives the base. So √3 * √3 = 3. Also remember that you can only add square roots together if they have the same base.