Question

Which of the following is equivalent to √405?
A) 4√5
B) 5√3
C) 9
D 9√5

Answer 1

The square root of 405 is equivalent to 9√5.

Step-by-step explanation:

The square root of 405 can be simplified by factoring it into its prime factors: 3 * 3 * 3 * 3 * 3 * 5. When grouped into pairs of factors, there are three pairs of 3s and one pair of 3s remains unpaired. Taking the square root of the paired factors gives us 3 * 3 * √5, which simplifies to 9√5. Therefore, the equivalent of √405 is 9√5, which is option D.

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