Pythagorean Theorem (& Simplify Radicals)

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What is the Pythagorean Theorem?

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The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².

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How do you simplify a radical expression?

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To simplify a radical expression, factor the number under the radical into its prime factors, and then pair the factors. Each pair can be taken out of the radical as a single factor.

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What is a radical?

Back

A radical is a symbol (√) that represents the root of a number. The most common radical is the square root.

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What does it mean to simplify √50?

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To simplify √50, factor it into √(25 * 2) = √25 * √2 = 5√2.

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Solve for x: x² = 119. What is x?

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x = √119.

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Find the simplified radical for x if x² = 52. What is x?

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x = √52 = 2√13.

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What is the approximate value of √115?

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√115 ≈ 10.7.

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Solve for x: x² = 88. What is x?

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x = √88 = 2√22.

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What is the simplified radical for x if x² = 84?

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x = √84 = 2√21.

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How do you approximate a radical?

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To approximate a radical, calculate its square root using a calculator or by estimating between two perfect squares.