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Popular >

simplify sqrt(120)

Solution

simplify

120

Solution

230

+1

Solution steps

120

Prime factorization of

120 : 2^{3} \cdot 3 \cdot 5

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

Apply exponent rule:

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

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

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

Apply radical rule:

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

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

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

Apply radical rule:

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

2^{2} = 2

= 2 2 \cdot 3 \cdot 5

Multiply the numbers:

2 \cdot 3 \cdot 5 = 30

= 230

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Frequently Asked Questions (FAQ)

What is sqrt(120) ?
The solution to sqrt(120) is 2sqrt(30)