How do you simplify a square root?

Find the largest perfect square that divides the number, and take its root outside.

When is a radical fully simplified?

When no perfect square factor is left under the root and no root is left in a denominator.

Split the number under the root into a perfect square times the rest: √72 = √36 · √2 = 6√2.

By Nethanel Bar, Co-founder & CEO

Last updated October 18, 2026

Write in simplest radical form.

12 problems

1.
√(72)
Solve on the board
Answer6×√(2)
1. Simplify the root
  6×√(2)
2.
√(52)
Solve on the board
Answer2×√(13)
1. Simplify the root
  2×√(13)
3.
8√(2) + 9√(2) − √(2)
Solve on the board
Answer16×√(2)
1. Collect like terms
  16×√(2)
4.
√(48)
Solve on the board
Answer4×√(3)
1. Simplify the root
  4×√(3)
5.
√(112)
Solve on the board
Answer4×√(7)
1. Simplify the root
  4×√(7)
6.
2√(3) + 9√(3) − √(3)
Solve on the board
Answer10×√(3)
1. Collect like terms
  10×√(3)
7.
√(76)
Solve on the board
Answer2×√(19)
1. Simplify the root
  2×√(19)
8.
√(90)
Solve on the board
Answer3×√(10)
1. Simplify the root
  3×√(10)
9.
7√(3) + 9√(3) − √(3)
Solve on the board
Answer15×√(3)
1. Collect like terms
  15×√(3)
10.
√(10) + √(40)
Solve on the board
Answer3×√(10)
1. Simplify the root
  √(10)+2×√(10)
2. Collect like terms
  3×√(10)
11.
√(8) + √(32)
Solve on the board
Answer6×√(2)
1. Simplify the root
  2×√(2)+√(32)
2. Simplify the root
  2×√(2)+4×√(2)
3. Collect like terms
  6×√(2)
12.
√(18) + √(32)
Solve on the board
Answer7×√(2)
1. Simplify the root
  3×√(2)+√(32)
2. Simplify the root
  3×√(2)+4×√(2)
3. Collect like terms
  7×√(2)

Like radicals combine the way like terms do: 3√2 + 4√2 = 7√2.

How do you simplify a square root?: Find the largest perfect square that divides the number, and take its root outside.
When is a radical fully simplified?: When no perfect square factor is left under the root and no root is left in a denominator.

Name: ____________________ Date: ____________

Write in simplest radical form.