Simplify square root of 161

Problem

√(,161)

Solution

1. Identify the number under the radical, which is 161

2. Check for divisibility by small prime numbers to find factors.

3. Test for 2: 161 is odd, so it is not divisible by 2

4. Test for 3: The sum of the digits is 1 + 6 + 1 = 8,w*h*i*c*h*i*s(n)*o*t*d(i)*v*i*s(i)*b*l*e*b*y,s(o)61i*s(n)*o*t*d(i)*v*i*s(i)*b*l*e*b*y$.

5. Test for 5: The last digit is not 0 or 5 so it is not divisible by 5

6. Test for 7: Divide 161 by 7

161÷7=23

7. Analyze the factors: Both 7 and 23 are prime numbers.

8. Determine if simplification is possible: Since 161=7×23 and there are no repeating prime factors (no perfect square factors), the square root cannot be simplified further into the form a√(,b)

Final Answer

√(,161)=√(,161)

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