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Popular >

simplify sqrt(4000)

Solution

simplify

4000

Solution

2010

+1

Decimal Notation

63.24555 \dots

Solution steps

4000

Prime factorization of

4000 : 2^{5} \cdot 5^{3}

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

Apply exponent rule:

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

2^{5} \cdot 5^{3} = 2^{4} \cdot 2 \cdot 5^{2} \cdot 5

= 2^{4} \cdot 2 \cdot 5^{2} \cdot 5

2^{4} \cdot 2 \cdot 5^{2} \cdot 5 = 2^{4} 5^{2} 2 \cdot 5

= 2^{4} 5^{2} 2 \cdot 5

2^{4} = 4

= 4 5^{2} 2 \cdot 5

Apply radical rule:

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

5^{2} = 5

= 4 \cdot 5 2 \cdot 5

Multiply the numbers:

4 \cdot 5 = 20

= 20 2 \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 2010

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∣ x + 5 ∣ = 7

Frequently Asked Questions (FAQ)

What is sqrt(4000) ?
The solution to sqrt(4000) is 20sqrt(10)