Calculate the square root of 245

Problem

√(,245)

Solution

1. Identify the number under the radical and look for its prime factors.

2. Factor the number 245 by checking for divisibility by small primes. Since it ends in 5, it is divisible by 5.

245=5×49

3. Recognize that 49 is a perfect square.

49=7

4. Rewrite the original expression using these factors.

√(,245)=√(,5×7)

5. Simplify the radical by moving the square root of the perfect square outside the radical sign.

√(,5×7)=7√(,5)

Final Answer

√(,245)=7√(,5)

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