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Popular >

simplify sqrt(27^3)

Solution

simplify

2 7^{3}

Solution

813

+1

Decimal Notation

140.29611 \dots

Solution steps

2 7^{3}

Apply exponent rule:

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

2 7^{2 + 1} = 2 7^{2} \cdot 27

= 2 7^{2} \cdot 27

Apply radical rule:

ab = a b, a \geq 0, b \geq 0

2 7^{2} \cdot 27 = 2 7^{2} 27

= 2 7^{2} 27

Apply radical rule:

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

2 7^{2} = 27

= 2727

Prime factorization of

27 : 3^{3}

= 27 3^{3}

Apply exponent rule:

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

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

= 27 3^{2} \cdot 3

Apply radical rule:

ab = a b, a \geq 0, b \geq 0

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

= 27 3^{2} 3

Apply radical rule:

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

3^{2} = 3

= 27 \cdot 33

Multiply the numbers:

27 \cdot 3 = 81

= 813

Popular Examples

2 \frac{4}{3}

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(x + 1)^{9}

Frequently Asked Questions (FAQ)

What is sqrt(27^3) ?
The solution to sqrt(27^3) is 81sqrt(3)