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Big Ideas Math Algebra 1 A Bridge to Success
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Big Ideas Math Algebra 1 A Bridge to Success View details
2. Radicals and Rational Exponents
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Exercise 3 Page 299

Think about the definition of a square root and a cubic root. How can you extend these definitions to define a general nth root?

See solution.

Practice makes perfect
Let's first think about how a square root and a cube root work so we can extend these operations to other types of roots. Recall that 2 is a square root of 4, since 2^2=4. This means that the square root operation will undo the squaring of a number. We denote this operation as shown below. sqrt(4) = sqrt(2^2) = 2

Furthermore, since 2^3=8, we can say that 2 is the cube root of 8, and we can think about the cube root as the operation that will undo the cubing of a number. sqrt(8) = sqrt(2^3) = 2 Note that we used the number 3 as an index in the radical sign to differ the cube root from the square root. Following the same way of thinking, in general, if a number a, when raised to the power n, equals a number b, this is b=a^n, and we can say that a is a nth root of b. sqrt(b) = sqrt(a^n) = a In other words, to calculate the nth root of b, which we denote as sqrt(b), we need to find the number a such that a^n=b.

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arrow_right Communicate Your Answer p.299
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arrow_right Monitoring Progress p.300-302
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arrow_right Exercises p.303-304
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