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Popular >

simplify sqrt(27000)

Solution

simplify

27000

Solution

3030

+1

Decimal Notation

164.31676 \dots

Solution steps

27000

Prime factorization of

27000 : 2^{3} \cdot 3^{3} \cdot 5^{3}

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

Apply exponent rule:

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

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

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

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

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

Apply radical rule:

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

2^{2} = 2

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

Apply radical rule:

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

3^{2} = 3

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

Apply radical rule:

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

5^{2} = 5

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

Multiply the numbers:

2 \cdot 3 \cdot 5 = 30

= 3030

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Frequently Asked Questions (FAQ)

What is sqrt(27000) ?
The solution to sqrt(27000) is 30sqrt(30)