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Popular >

simplify 4sqrt(216)

Solution

simplify

4216

Solution

246

+1

Decimal Notation

58.78775 \dots

Solution steps

4216

Prime factorization of

216 : 2^{3} \cdot 3^{3}

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

Apply exponent rule:

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

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

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

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

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

Apply radical rule:

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

2^{2} = 2

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

Apply radical rule:

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

3^{2} = 3

= 4 \cdot 2 \cdot 3 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 4 \cdot 66

Multiply the numbers:

4 \cdot 6 = 24

= 246

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Frequently Asked Questions (FAQ)

What is 4sqrt(216) ?
The solution to 4sqrt(216) is 24sqrt(6)