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How to Solve for Square Roots of Radical Expressions

A square root of a number is a value that, when multiplied times itself, equals the original number. A radical expression is a mathematical expression that contains a radical and a radicand. The radical is the symbol that resembles a check mark and indicates that a root will be calculated. The number beneath the radical symbol is the radicand. This is the value from which the root will be calculated. If there is no number on the upper left side of the radical, you must calculate the square root of the expression.

Instructions

    • 1

      Solve perfect squares in a radical expression by simply extracting the square root. If the expression is a simple one, such as √4 or √25, solve it just by remembering what number times itself equals those radicands. In this case, √4 equals 2, and √25 equals 5. If the number is larger, you may want to press the radical symbol on your calculator or use an online square root calculator.

    • 2

      Simplify a radical expression by extracting its factors and looking for square roots. For example, if consider the expression √72. You can restate √72 as √36 * √2. Since 36 is a perfect square, extract 6 from this part of the equation. Therefore, your answer would be 6√2.

    • 3

      Solve a fractional radical expression with a square root in the denominator by multiplying the numerator and denominator by the square root itself. For example, consider the expression x/√y. Multiply the top and bottom of the fraction by √y. When you multiply two square roots, your answer is the radicand without the radical sign. In this case, √y * √y equals y. Therefore, your answer would be x√y/y.

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