Evaluate square root of 405

Problem

√(,405)

Solution

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

2. Factor the number 405 by checking for divisibility. Since the digits sum to 9 (4 + 0 + 5 = 9),t*h*e*n*u*m*b*e*r*i*s(d(i))*v*i*s(i)*b*l*e*b*y$.

405=9×45

3. Continue factoring the remaining part to find the largest perfect square factor.

45=9×5

4. Combine the factors to express 405 as a product of a perfect square and a non-perfect square.

405=81×5

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

√(,405)=√(,81×5)

6. Simplify the square root of the perfect square.

√(,81)=9

Final Answer

√(,405)=9√(,5)

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