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Popular >

simplify sqrt(54)

Solution

simplify

54

Solution

36

+1

Decimal

7.34846 \dots

Solution steps

54

Prime factorization of

54 : 2 \cdot 3^{3}

= 2 \cdot 3^{3}

Apply exponent rule:

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

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

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

Apply radical rule:

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

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

= 3^{2} 2 \cdot 3

Apply radical rule:

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

3^{2} = 3

= 3 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 36

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Frequently Asked Questions (FAQ)

What is sqrt(54) ?
The solution to sqrt(54) is 3sqrt(6)