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There is a partial relationship.

The principal square root of a perfect square is the number itself.

For example,

the principal square root of 5^2

= the principal square root of 25

= the positive element in {-5, 5}

= 5.

The converse is not true. The number 3, for example, has a square root which are approx -1.7321 and 1.7321. But the square of either of these numbers is 3, but that is not a perfect square since it is not the square of an integer.

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Q: What is the relationship between perfect squares and square roots examples?

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The square roots of perfect squares are the numbers that when squared create perfect squares as for example 36 is a perfect square and its square root is 6 which when squared is 36

683 perfect squares.

10 perfect squares

sqrt(2000) = 44.7sqrt(20000) = 141.4So the perfect squares between 2000 and 20000 are the squares of 45 to 141 (inclusive)ie there are 97 perfect squares in the interval.

Two. 36, and 49 are perfect squares.

1,4,9,16,25,36,49,64,81,100,121,144,169,196.

Perfect square roots are the counting numbers {1, 2, 3, ...} The squares of the perfect square roots are the perfect squares, namely 1² = 1, 2² = 4, 3² = 9, etc.

There are 8: the squares of 2 to 9, inclusive.

Eight.

There are twelve.

1,4,9,16,25,36,49,64,81

There are 24 perfect squares between 50 and 1000.

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