What is the definition of a perfect square?

A perfect square is an integer that is the square of another integer. For example, 1, 4, 9, 16, and 25 are perfect squares because they are 1², 2², 3², 4², and 5², respectively.

If x² = 36, what are the possible values of x?

The possible values of x are 6 and -6 because both (6)² and (-6)² equal 36.

Solve for y: y² - 16 = 0.

Hint: Factor the equation.

Factor the equation: (y - 4)(y + 4) = 0. Setting each factor to zero gives y - 4 = 0 or y + 4 = 0, so y = 4 or y = -4.

Calculate the value of √(81).

The value of √(81) is 9, since 9² = 81.

If a perfect square ends with 4, what can be said about the last digit of the number whose square it is?

If a perfect square ends with 4, the last digit of the number whose square it is can either be 2 or 8, since (2)² = 4 and (8)² = 64.

If x² - 9 = 0, what are the solutions for x?

Hint: Factor the expression.

Factor the expression: (x - 3)(x + 3) = 0. Thus, x = 3 or x = -3.

What is the sum of the square roots of 16 and 25?

The sum is √16 + √25 = 4 + 5 = 9.

What is the relationship between squares and square roots?

The square of a number is the product of the number multiplied by itself, while the square root of a number is the value that, when multiplied by itself, gives the original number.

What is the square root of 64?

The square root of 64 is 8, since 8² = 64.