What is 5sqrt(a^2*b^2*c^2) ?

The solution to 5sqrt(a^2*b^2*c^2) is 5abc

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simplify 5sqrt(a^2b^2c^2)

simplify

5 a^{2} \cdot b^{2} \cdot c^{2}

5 ab c

Solution steps

5 a^{2} b^{2} c^{2}

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

a^{2} b^{2} c^{2} = a^{2} b^{2} c^{2}

= 5 a^{2} b^{2} c^{2}

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

b^{2} c^{2} = b^{2} c^{2}

= 5 a^{2} b^{2} c^{2}

Apply radical rule:

a^{2} = a,

assuming

a \geq 0

a^{2} = a

= 5 a b^{2} c^{2}

Apply radical rule:

a^{2} = a,

assuming

a \geq 0

b^{2} = b

= 5 ab c^{2}

Apply radical rule:

a^{2} = a,

assuming

a \geq 0

c^{2} = c

= 5 ab c

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