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Popular >

simplify sqrt(36^3)

Solution

simplify

3 6^{3}

Solution

216

Solution steps

3 6^{3}

Apply exponent rule:

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

3 6^{2 + 1} = 3 6^{2} \cdot 36

= 3 6^{2} \cdot 36

Apply radical rule:

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

3 6^{2} \cdot 36 = 3 6^{2} 36

= 3 6^{2} 36

Apply radical rule:

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

3 6^{2} = 36

= 3636

Prime factorization of

36 : 2^{2} \cdot 3^{2}

= 36 2^{2} \cdot 3^{2}

Apply radical rule:

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

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

= 36 2^{2} 3^{2}

Apply radical rule:

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

2^{2} = 2

= 36 \cdot 2 3^{2}

Apply radical rule:

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

3^{2} = 3

= 36 \cdot 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 36 \cdot 6

Multiply the numbers:

36 \cdot 6 = 216

= 216

Popular Examples

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Frequently Asked Questions (FAQ)

What is sqrt(36^3) ?
The solution to sqrt(36^3) is 216