Evaluate square root of 1988

Problem

√(,1988)

Solution

1. Identify the number under the radical and look for perfect square factors.

2. Factor the number 1988 by checking for divisibility. Since the last two digits are 88 the number is divisible by 4

1988=4×497

3. Check if 497 has any other perfect square factors. Testing small primes: 497 is not divisible by 2 3 (4+9+7=20, or 5 Testing 7

497=7×71

4. Determine if 71 is prime. Since 71 is not divisible by 2, 3, 5, 7(i*t*i*s()) \times 10 + 1),o*r1(i*t*i*s())1 \times 6 + 5),a*n*dsqrt{71} \approx 8.4,w*e*c*o*n*c*l*u*d(e)1$ is prime.

5. Apply the product property of radicals √(,a×b)=√(,a)×√(,b) to simplify the expression.

√(,1988)=√(,4×497)

√(,1988)=√(,4)×√(,497)

6. Simplify the square root of the perfect square.

√(,4)=2

Final Answer

√(,1988)=2√(,497)

Want more problems? Check here!