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Another way of looking at square roots

Think of looking at square roots as finding the number of columns or rows a square has.

Square roots are the numbers that have been turned into squares. They are the opposite of exponents.

Square roots are usually found using the radical sign, which is $ \sqrt{}\, $, though it can be found using the exponent $ n^\frac{1}{2}\, $.

Perfect SquaresEdit

Below is a list of the first ten perfect squares whose answers are whole numbers.

  • $ \sqrt{1}\, = 1 $
  • $ \sqrt{4}\, = 2 $
  • $ \sqrt{9}\, = 3 $
  • $ \sqrt{16}\, = 4 $
  • $ \sqrt{25}\, = 5 $
  • $ \sqrt{36}\, = 6 $
  • $ \sqrt{49}\, = 7 $
  • $ \sqrt{64}\, = 8 $
  • $ \sqrt{81}\, = 9 $
  • $ \sqrt{100}\, = 10 $

Irrational SquaresEdit

Some square roots turn out to be irrational numbers.

  • $ \sqrt{2}\, = 1.41421356237309... $
  • $ \sqrt{3}\, = 1.73205080756887... $
  • $ \sqrt{5}\, = 2.23606797749979... $
  • $ \sqrt{6}\, = 2.449489742783178... $
  • $ \sqrt{7}\, = 2.645751311064591... $

Imaginary SquaresEdit

Some square roots turn out to be imaginary numbers.

  • $ \sqrt{-9}\, = 3i $
  • $ \sqrt{-5}\, = i\sqrt{5}\, $

The square roots of negative numbers are always imaginary numbers; they have no real answer. The only way to obtain real answers from negative numbers are with cubic roots.

See AlsoEdit

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