What is sqrt(z)sqrt(30z^2)sqrt(35z^3) ?

The solution to sqrt(z)sqrt(30z^2)sqrt(35z^3) is 5sqrt(42)z^3

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simplify sqrt(z)sqrt(30z^2)sqrt(35z^3)

simplify

z 30 z^{2} 35 z^{3}

542 z^{3}

Solution steps

z 30 z^{2} 35 z^{3}

Simplify

30 z^{2} : 30 z

= z 30 z 35 z^{3}

Simplify

35 z^{3} : 35 z z

= z 30 z 35 z z

Apply radical rule:

a a = a,

assuming

a \geq 0

z z = z

= z 30 z 35 z

Apply exponent rule:

aa = a^{2}

zz = z^{2}

= z 30 z^{2} 35

Simplify

z z^{2} : z^{3}

= z^{3} 3035

= 3035 z^{3}

30 = 56

= 5635 z^{3}

35 = 57

= 5657 z^{3}

Apply radical rule:

a a = a, a \geq 0

55 = 5

= 567 z^{3}

67 = 42

= 542 z^{3}

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What is sqrt(z)sqrt(30z^2)sqrt(35z^3) ?
The solution to sqrt(z)sqrt(30z^2)sqrt(35z^3) is 5sqrt(42)z^3