Evaluate square root of 31500

Problem

√(,31500)

Solution

1. Factor the number inside the square root into a product of a perfect square and other factors.

31500=315×100

2. Identify further factors of 315 to find more perfect squares.

315=5×63

63=9×7

3. Combine all factors to see the full prime factorization or perfect square components.

31500=100×9×5×7

31500=900×35

4. Apply the product property of square roots, √(,a×b)=√(,a)×√(,b)

√(,31500)=√(,900×35)

5. Simplify by taking the square root of the perfect square.

√(,900)=30

√(,31500)=30√(,35)

Final Answer

√(,31500)=30√(,35)

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