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Popular >

simplify sqrt(3000)

Solution

simplify

3000

Solution

1030

+1

Decimal Notation

54.77225 \dots

Solution steps

3000

Prime factorization of

3000 : 2^{3} \cdot 3 \cdot 5^{3}

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

Apply exponent rule:

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

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

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

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

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

Apply radical rule:

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

2^{2} = 2

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

Apply radical rule:

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

5^{2} = 5

= 2 \cdot 5 2 \cdot 3 \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 10 2 \cdot 3 \cdot 5

Multiply the numbers:

2 \cdot 3 \cdot 5 = 30

= 1030

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Frequently Asked Questions (FAQ)

What is sqrt(3000) ?
The solution to sqrt(3000) is 10sqrt(30)