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Wize High School Grade 9 Math Textbook > Polynomial Expressions

The Meaning of xx, x2x^2, x3x^3, and x\sqrt x

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The Meaning of Squares, Cubes, and Square Roots

The variable xx can represent any quantity, but if we let xx represent the length of a physical object, then we will have a physical meaning for x2x^2, x3x^3, and x\sqrt x.

1 Dimension - Lengths

xx represents the length measurement in 1 dimension

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2 Dimensions - Squares

x2x^2 represents the area measurement of a square in 2 dimensions

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3 Dimensions - Cubes

x3x^3 represents the volume measurement of a cube in 3 dimension

Square Roots

x2=x\sqrt{x^2}=x, which is the length of the square! So we can think of ...\sqrt{...} as finding the length of a square with area .......

Example
25\sqrt {25} represents the length of the square that has area 2525

Practice: Powers, Square Roots, and their Physical Meaning

Enter the expression that represents the quantity indicated.
The length of the line