Question

Sqrt(5x^2)×sqrt(40x)

Answer 1

Find the prime factorizations: \(\sqrt{5*40*x^2*x}\)

Answer 2

\[=\sqrt(5)*\sqrt(x^2)*\sqrt(40)*\sqrt(x) \]
Combine constants multiplicatively
\[ =\sqrt(200)*x*\sqrt(x) \]
combine powers of x (\sqrt = ^1/2) and extract factor of 4 from 200 [= 4*50]
\[ =2*\sqrt(50)*x^{3/2} \]
50 = 2*25 = 2*(5^2), so extract 5
\[= 10*\sqrt(2)*x^{3/2}\]


\[x\]

Answer 3

Look for factors,don't just multiply willy-nilly.

\(\sqrt{5*40*x^{2}*x}\)

We know that x >= 0.

\(x\sqrt{5*40*x}\)

There's a factor of 5 in 40.

\(5x\sqrt{8*x}\)

There's a factor of 4 in 8.

\(10x\sqrt{2*x}\)

And it's done.