What is sqrt(8x^2yz^2)sqrt(yzw)sqrt(2zw^3) ?

The solution to sqrt(8x^2yz^2)sqrt(yzw)sqrt(2zw^3) is 4xyz^2w^2

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simplify sqrt(8x^2yz^2)sqrt(yzw)sqrt(2zw^3)

simplify

8 x^{2} y z^{2} yz w 2 z w^{3}

4 x y z^{2} w^{2}

Solution steps

8 x^{2} y z^{2} yz w 2 z w^{3}

Simplify

8 x^{2} y z^{2} : 22 x y z

= 22 x y z yz w 2 z w^{3}

Simplify

yz w : y z w

= 22 x y z y z w 2 z w^{3}

Simplify

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

= 22 x y z y z w 2 z w w

Apply radical rule:

a a = a, a \geq 0

22 = 2

= 2 \cdot 2 x y z y z w z w w

Apply radical rule:

a a = a,

assuming

a \geq 0

y y = y

= 2 \cdot 2 x yz z w z w w

Apply radical rule:

a a = a,

assuming

a \geq 0

z z = z

= 2 \cdot 2 x yzz w w w

Apply radical rule:

a a = a,

assuming

a \geq 0

w w = w

= 2 \cdot 2 x yzz ww

Multiply the numbers:

2 \cdot 2 = 4

= 4 x yzz ww

Apply exponent rule:

aa = a^{2}

zz = z^{2}

= 4 x y z^{2} ww

Apply exponent rule:

aa = a^{2}

ww = w^{2}

= 4 x y z^{2} w^{2}

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- 296 + 176

3 x - 7 = 32

4 ∣ 6 - 2 a ∣ + 8 \leq 24

What is sqrt(8x^2yz^2)sqrt(yzw)sqrt(2zw^3) ?
The solution to sqrt(8x^2yz^2)sqrt(yzw)sqrt(2zw^3) is 4xyz^2w^2