How to find the square root 2000?

Question

Hayley Rosario · Accepted Answer

Step 1 Find the square root using prime factorization method: The prime factors of

2000

are

2000 = 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5

Step 2
Thus, the square root of 2000 is

2000 = 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5

\Rightarrow \sqrt{2000} = \sqrt{2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5}

\Rightarrow \sqrt{2000} = 2 \times 2 \times 5 \times \sqrt{5}

\Rightarrow \sqrt{2000} = 20 \sqrt{5}

Thus, the square root of 2000 is

20 \sqrt{5}

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