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$4⋅4-4⋅(-4) =16=16 $

All positive numbers have two square roots — one positive and one negative. To avoid ambiguity, when talking about $4 $is used. For example, the square root of $16$ is denoted as

$16 .$

$16 =4 $

In the example above, the principal root of $16$ is $4$ because $4$ multiplied by itself equals $16$ and $4$ is positive. When a number is a perfect square, its square roots are integers. The square roots of positive integers that are non-perfect squares are irrational numbers. Principal Root of Perfect Squares | Principal Root of Non-Perfect Squares | ||
---|---|---|---|

Perfect Square | Principal Root (Integer Number) |
Non-Perfect Square | Principal Root (Irrational Number) |

$1$ | $1 =1$ | $2$ | $2 ≈1.414213…$ |

$4$ | $4 =2$ | $3$ | $3 ≈1.732050…$ |

$9$ | $9 =3$ | $5$ | $5 ≈2.236067…$ |

$16$ | $16 =4$ | $10$ | $10 ≈3.162277…$ |

$25$ | $25 =5$ | $20$ | $20 ≈4.472135…$ |

$a⋅a≥0,for any real numbera $

Instead, the square roots of negative numbers are imaginary numbers.
Separate from whole numbers, the square roots of fractions can be calculated by taking square roots of the numerator and denominator separately. Consider the following example.

$169 =4_{2}3_{2} ⇒169 =43 $

The square roots of decimal numbers can be calculated by writing them in the fraction form. Then, the square roots of the numerator and denominator are calculated. Consider the following example.
$0.36=10036 =10_{2}6_{2} ⇓10036 =106 =0.6 $