Estimating square roots

Estimating square roots

Estimating square roots

Most numbers are not perfect squares, so their square roots are not whole numbers. For example √20 is not a whole number — but we can still say roughly how big it is.

Trap it between two perfect squares

To estimate √20, find the perfect squares just below and just above 20:

16 < 20 < 25, so √16 < √20 < √25, which means 4 < √20 < 5.

So √20 is between 4 and 5. Because 20 is closer to 16 than to 25, √20 is a bit above 4 — about 4.5. (A calculator gives 4.47.)

Rounding to the nearest whole number

If a question asks for the nearest whole number, pick the closer of the two boundaries. Here 20 is closer to 16, so √20 rounds to 4.

Three rules that always help

  • Find the perfect square just below and just above the number.
  • The square root lies between the two whole-number roots of those perfect squares.
  • Compare the gaps to decide which whole number it is closer to.

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