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Popular >

simplify sqrt(32000)

Solution

simplify

32000

Solution

805

+1

Decimal Notation

178.88543 \dots

Solution steps

32000

Prime factorization of

32000 : 2^{8} \cdot 5^{3}

= 2^{8} \cdot 5^{3}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

2^{8} \cdot 5^{3} = 2^{8} \cdot 5^{2} \cdot 5

= 2^{8} \cdot 5^{2} \cdot 5

2^{8} \cdot 5^{2} \cdot 5 = 2^{8} 5^{2} 5

= 2^{8} 5^{2} 5

2^{8} = 16

= 16 5^{2} 5

Apply radical rule:

a^{2} = a, a \geq 0

5^{2} = 5

= 16 \cdot 55

Multiply the numbers:

16 \cdot 5 = 80

= 805

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Frequently Asked Questions (FAQ)

What is sqrt(32000) ?
The solution to sqrt(32000) is 80sqrt(5)