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 x^4=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 10^4 to estimate the range. Since 10^4=10000 the answer must be less than 10

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

7^2=49

49^2=(50−1)^2

49^2=2500−100+1

49^2=2401

5. Conclude that since 7^4=2401 the fourth root is 7

Final Answer

√(4,2401)=7

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