What is factor sqrt(32x^4y^5) ?

The solution to factor sqrt(32x^4y^5) is 4sqrt(2)x^2y^2sqrt(y)

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factor sqrt(32x^4y^5)

factor

32 x^{4} y^{5}

42 x^{2} y^{2} y

Solution steps

32 x^{4} y^{5}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 32 x^{4} y^{5}

32 = 42

= 42 x^{4} y^{5}

Apply exponent rule:

a^{b c} = (a^{b})^{c}

x^{4} = x^{2 \cdot 2} = (x^{2})^{2}

= 42 (x^{2})^{2} y^{5}

Apply radical rule:

assuming

a \geq 0

(x^{2})^{2} = x^{2}

= 42 x^{2} y^{5}

Apply exponent rule:

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

= 42 x^{2} y^{4} y^{1}

Apply radical rule:

a \cdot b = a b

= 42 x^{2} y^{4} y^{1}

Apply exponent rule:

a^{b c} = (a^{b})^{c}

y^{4} = y^{2 \cdot 2} = (y^{2})^{2}

= 42 x^{2} (y^{2})^{2} y^{1}

Apply radical rule:

assuming

a \geq 0

(y^{2})^{2} = y^{2}

= 42 x^{2} y^{2} y^{1}

Apply rule

a^{1} = a

y^{1} = y

= 42 x^{2} y^{2} y

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What is factor sqrt(32x^4y^5) ?
The solution to factor sqrt(32x^4y^5) is 4sqrt(2)x^2y^2sqrt(y)