Square Root Calculator
The square root of a number is the value that, multiplied by itself, gives that number. Get the decimal value, and for whole numbers the exact simplified radical your teacher wants.
Answer
≈ 8.48528137
Step by step
- Find the largest perfect square that divides 72: 36 (6²).
- Split it: √72 = √(36 × 2) = √36 × √2.
- √36 = 6, so √72 = 6√2.
- Estimate: 8² = 64 and 9² = 81, so √72 is between 8 and 9.
- Decimal value: √72 ≈ 8.48528137.
Answer: 6√2
Still stuck? Ask the tutor about these steps
How it works
√x = y means y × y = x√(a² × b) = a√bPerfect squares (1, 4, 9, 16, 25, 36, 49, 64, 81, 100…) have whole-number roots.
To simplify a root, find the biggest perfect square that divides the number, take its root outside, and leave the rest inside: √72 = √(36 × 2) = 6√2.
To estimate, find the perfect squares on either side: √50 is a bit more than 7 because 7² = 49.
Worked example
Simplify √72.
- 72 = 36 × 2, and 36 is a perfect square
- √72 = √36 × √2
- = 6√2 ≈ 8.485
Frequently asked questions
How do you simplify a square root?
Pull out the largest perfect-square factor: √48 = √(16 × 3) = 4√3.
What is the square root of 2?
About 1.41421356. It is irrational: the decimals go on forever without repeating.
Does a square root have two answers?
Every positive number has two square roots, like +5 and −5 for 25. The √ symbol means the positive one, which is what this calculator gives.