Evaluate fourth root of 2401

Problem

√(4,2401)

Solution

1. Identify the number under the radical and the index of the root. We are looking for a number x such that x4=2401

2. Test small integers ending in digits that, when raised to the fourth power, result in a number ending in 1 These digits are 1, 3, 7,a*n*d$.

3. Calculate 10 to estimate the range. Since 10=10000 the answer must be less than 10

4. Evaluate 7 by squaring 7 and then squaring the result.

7=49

49=(50−1)2

49=2500−100+1

49=2401

5. Conclude that since 7=2401 the fourth root is 7

Final Answer

√(4,2401)=7

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