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Popular >

simplify 5sqrt(108)

Solution

simplify

5108

Solution

303

+1

Decimal Notation

51.96152 \dots

Solution steps

5108

Prime factorization of

108 : 2^{2} \cdot 3^{3}

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

Apply exponent rule:

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

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

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

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

= 5 2^{2} 3^{2} 3

Apply radical rule:

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

2^{2} = 2

= 5 \cdot 2 3^{2} 3

Apply radical rule:

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

3^{2} = 3

= 5 \cdot 2 \cdot 33

Multiply the numbers:

2 \cdot 3 = 6

= 5 \cdot 63

Multiply the numbers:

5 \cdot 6 = 30

= 303

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Frequently Asked Questions (FAQ)

What is 5sqrt(108) ?
The solution to 5sqrt(108) is 30sqrt(3)