Evaluate fourth root of 6561

Problem

√(4,6561)

Solution

1. Identify the number as a power of a smaller integer. Since the number ends in 1, the base likely ends in 1, 3, 7, or 9.

2. Test the number 9, as 9=81

3. Calculate the square of 81 to see if it equals 6561.

81×81=6561

4. Rewrite the expression using the property of exponents where √(4,x)=(x(1/4))

√(4,6561)=(81)(1/4)

5. Simplify the exponents by multiplying them.

(81)(1/4)=81(2/4)

81(1/2)=√(,81)

6. Evaluate the square root of 81.

√(,81)=9

Final Answer

√(4,6561)=9

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