Square Root Calculator

The square root of a number is the value that gives that number when multiplied by itself. This square root calculator gives exact answers in simplified surd form, such as √50 = 5√2, along with the decimal. It shows the prime factorisation and how pairs of factors come out of the root.

Try:

How to use the square root calculator

  1. Enter a number, such as 50, 144 or 2.25.
  2. Press Calculate.
  3. Read the exact simplified root, the decimal and the steps.

Formula

a2b=ab\sqrt{a^2 b} = a\sqrt{b}
ab=ab\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}

Worked example: √50

  • Number: 50

✓ Answer checked

525\sqrt{2}
Decimal
≈7.071067812\approx 7.071067812
Step-by-step working (4 steps)

  1. Find the prime factors Prime factorisation

    Break the number into prime factors.

    50=2×5250 = 2 \times 5^{2}

  2. Pair up equal factors √(a²b) = a√b

    Each pair of equal factors comes out of the root as one factor.

    50=52×2\sqrt{50} = \sqrt{5^2 \times 2}

  3. Simplify

    2 has no square factors left, so it stays under the root.

    50=52\sqrt{50} = 5\sqrt{2}

  4. Decimal value

    Work out the decimal and round it.

    52≈7.0710678125\sqrt{2} \approx 7.071067812
Formulas used
a2b=ab\sqrt{a^2 b} = a\sqrt{b}
How this was checked
  • ✓ Squaring the answer: (5)² × 2 = 50.
  • ✓ Decimal check: 7.071067812² ≈ 50.

Frequently asked questions

How do I simplify a square root?

Write the number as a product of primes and take out each pair. 50 = 2 × 5 × 5, so √50 = 5√2.

What is a perfect square?

A whole number whose square root is also a whole number, such as 1, 4, 9, 16 and 144.

Can you take the square root of a negative number?

Not as a real number. The calculator gives the answer using the imaginary unit i, where i² = −1, so √−9 = 3i.

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