Practice Radical Operations in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Adding, subtracting, and multiplying expressions that contain radicals. Like terms (same radicand) can be combined for addition and subtraction; for multiplication, use a⋅b=ab.

Treat simplified radicals like variables: 35+25=55 works just like 3x+2x=5x. You can only combine radicals with the SAME radicand. Multiplication is more flexible since a⋅b=ab always works.

Showing a random 20 of 50 problems.

Example 1

medium
Expand (3+2)(3−2).

Example 2

medium
Multiply 6⋅10 and simplify.

Example 3

medium
Simplify 20+35.

Example 4

hard
Simplify 200+98−8.

Example 5

easy
Simplify 52+2.

Example 6

hard
Simplify (32−8)2.

Example 7

easy
Multiply 5⋅7.

Example 8

easy
Multiply 2⋅18.

Example 9

easy
Simplify 35+75.

Example 10

easy
Multiply 11⋅11.

Example 11

hard
Expand and simplify (3+2)(3−2).

Example 12

medium
Simplify 182.

Example 13

hard
Solve for a: a2+32=102.

Example 14

challenge
Simplify (2+3+6)2−(2+3)2.

Example 15

easy
Simplify 6⋅6.

Example 16

medium
Simplify 502.

Example 17

easy
Simplify 35+25.

Example 18

easy
Multiply 2⋅8.

Example 19

hard
Expand and simplify (8+2)(18−2).

Example 20

easy
Multiply 3⋅12.