Question

How do you simplify `sqrt(8x^5)* sqrt(10x^3)`?

Answer 1

`sqrt(8x^5) * sqrt(10x^3)=color(blue)(4sqrt(5)x^4)`

Explanation:

`sqrt(8x^5) * sqrt(10x^3)`

`color(white)("XXX")=sqrt(8 * 10 * x^5 * x^3)`

`color(white)("XXX")=sqrt( 80 * x^8)`

`color(white)("XXX")=sqrt(4^2 * 5 * (x^4)^2)`

`color(white)("XXX")=4sqrt(5)x^4`

Answer 2

`4 sqrt 5 x^4`

Explanation:

`sqrt (8 x^5) * sqrt (10 x^3)`

`= sqrt (8 x^5*10 x^3)`

`= sqrt (80 x^8)`

`= sqrt ((4 x^4)^2*5)`

`= 4 sqrt 5 x^4` [Ans]

Answer 3

`4 sqrt 5 x^4`

Explanation:

`sqrt (8 x^5)* sqrt (10 x^3)`

`:.8^(1/2)* (x^5)^(1/2)* 10^(1/2)*(x^3)^(1/2)`

`:.2^(1/2)*2^(1/2)*2^(1/2)*x^(5/2)*2^(1/2)*5^(1/2)*x^(3/2)`

`:.2^(4/2)*x^(8/2)*5^(1/2)`

`:.2^2*x^4*sqrt 5`

`:.4 sqrt 5 x^4`