(√5 * √20) 2 = ? Surd Question

(√5 * √20)^2  = ?

 

How do I answer the above in detail?

 

(√5 * √20)^2  =100

 

Simplify the following:
(sqrt(5) sqrt(20))^2

sqrt(20)  =  sqrt(4×5)  =  sqrt(2^2×5):
(sqrt(5) sqrt(2^2 5))^2

sqrt(2^2 5)  =  sqrt(2^2) sqrt(5)  =  2^(2/2) sqrt(5)  =  2 sqrt(5):
(sqrt(5)×2 sqrt(5))^2

sqrt(5)×2 sqrt(5) = 5×2:
5×2^2

Multiply each exponent in 5×2 by 2:
5^2×2^2

2^2 = 4:
5^2×4

5^2 = 25:
25×4

25×4  =  100:
Answer: | 
| 100

\((\sqrt5*\sqrt{20})^2\\ =(\sqrt{100})^2\\ =100 \)

 

The square root and the square cancel each other out :)