What is sqrt(2a)*sqrt(14a^3)*sqrt(5a) ?

The solution to sqrt(2a)*sqrt(14a^3)*sqrt(5a) is 2sqrt(35)a^{5/2}

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simplify sqrt(2a)sqrt(14a^3)sqrt(5a)

simplify

2 a \cdot 14 a^{3} \cdot 5 a

235 a^{\frac{5}{2}}

Solution steps

2 a 14 a^{3} 5 a

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

2 a = 2 a

= 2 a 14 a^{3} 5 a

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

5 a = 5 a

= 25 a a 14 a^{3}

Apply radical rule:

a a = a

a a = a

= 25 a 14 a^{3}

14 a^{3} : 14 a^{\frac{3}{2}}

= 214 a^{\frac{3}{2}} 5 a

Factor integer

14 = 2 \cdot 7

= 2 2 \cdot 7 a^{\frac{3}{2}} 5 a

Apply radical rule:

2 \cdot 7 = 27

= 227 a^{\frac{3}{2}} 5 a

Apply radical rule:

a a = a

22 = 2

= 275 a a^{\frac{3}{2}}

Apply exponent rule:

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

a^{\frac{3}{2}} a = a^{\frac{3}{2} + 1}

= 275 a^{\frac{3}{2} + 1}

a^{\frac{3}{2} + 1} = a^{\frac{5}{2}}

= 275 a^{\frac{5}{2}}

Apply radical rule:

a b = a \cdot b

75 = 7 \cdot 5

= 2 7 \cdot 5 a^{\frac{5}{2}}

Multiply the numbers:

7 \cdot 5 = 35

= 235 a^{\frac{5}{2}}

40 \cdot 2

\frac{16}{- 8}

2^{l o g_{2} (10)}

2^{3 + l o g_{2} (5)}

(- 2 x y) (- 2 x y)

What is sqrt(2a)*sqrt(14a^3)*sqrt(5a) ?
The solution to sqrt(2a)*sqrt(14a^3)*sqrt(5a) is 2sqrt(35)a^{5/2}