Roots & Equations with Exponents Review

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What is a perfect square?

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A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16, and 25 are perfect squares.

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What is the square root of a number?

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The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 x 3 = 9.

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What does it mean if an equation has no real solutions?

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An equation has no real solutions if there are no values of the variable that satisfy the equation. For example, @@ ext{the equation } \\sqrt{-64} ext{ has no real solutions.}$$

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How do you estimate the square root of a non-perfect square?

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To estimate the square root of a non-perfect square, find the two perfect squares it lies between and then approximate. For example, @@ ext{to estimate } \\sqrt{61}, ext{ note that } 49 < 61 < 64, ext{ so } 7 < \\sqrt{61} < 8.$$

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What is a radical expression?

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A radical expression is an expression that includes a root, such as a square root or cube root. For example, @@ ext{the expression } \\sqrt{x} ext{ is a radical expression.}$$

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What is the difference between rational and irrational numbers?

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Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot be expressed as a simple fraction. For example, @@ ext{ } \\sqrt{2} ext{ is irrational.}$$

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What is the definition of an exponent?

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What is the square of a negative number?

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