Perfect squares and roots

Perfect squares

1 is the square root of 1 2 is the square root of 2 3 is the square root of 9 4 is the square root of 16 5 is the square root of 25 6 is the square root of 36 7 is the square root of 49 8 is the square root of 64 9 is the square root of81 10 is the square root of 100 11 is the square root of 121 12 is the square root of 144

Perfect squares

Only a few whole numbers, called perfect squares, have exact square roots. For example, the square root of 25 is 5.

other roots do exist

cube roots 2x2x2 fourth roots 2x2x2x2 fifth roots 2x2x2x2x2 and so on

Irrational numbers

other whole numbers have square roots that are decimals that go on forever and have no pattern that repeat (nonrepeating, nonterminating decimals), so they're called irrational numbers. The square root of 30 is 5.4772255 with no end to the decimal places.

Irrational numbers

suppose you run across square root of 54 square root of 64 is 8 square root of 49 is 7 so you know your number is between these two 7.4 x 7.4 = 54.76 The best answer is usually the one that does not go over to the nearest tenth. 7.3 x 7.3 = 53.29 Your square root of 54 would then be 7.3

the cube root of 27 is 3 3 x 3 x 3 = 27

the fourth root of 16 is 2 2 x 2 x 2 x 2 = 16

a square root is the factor of a number that, when multiplied by itself, produces the number. Take the number 36, for example. One of the factors of 36 is 6. If you multiply 6 by itself (6 x 6), you come up with 36, so 6 is the square root of 36. The number 36 has other factors, such as 18. But if you multiply 18 by itself (18 x 18), you get 324, not 36. So 18 isn't the square root of 36.

to find the square root of any number simply multiply. 20 x 20 = 400. Now you have the square root of 400, which is 20. Every number has a square root. Some are just easier to find than others.