Question

Step by step solution/explanation needed ASAP

Answer 1

a) 2

b)
`(4x)/(y)`

Explanation:

a)
`(√(500) )/(√(5) )`

We can rewrite 500 as 100*5 and 100 is
`10^2` causing the 10 to come out of the root.

`(10√(5) )/(√(5) )`

Rationalize.

`(10√(5) )/(√(5) )*(√(5) )/(√(5) ) =(10)/(5)=2`

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b)
`(√(48x^3) )/(√(3xy^2) )`

48 can be rewritten as 6*8 and 8 can be rewritten as
`2^2*2`

`(√(6*2^2*2x^3) )/(√(3xy^2) )`

`(2√(6*2x^3) )/(√(3xy^2) )`

`(2√(12x^3) )/(√(3xy^2) )`

12 can be rewritten as 4*3 and 4 can be rewritten as
`2^2`

`(2√(2^2*3x^3) )/(√(3xy^2) )`

`(2*2√(3x^3) )/(√(3xy^2) )`

`(4√(3x^3) )/(√(3xy^2) )`

`x^3` is the same as
`x^2*x` causing x to come out of the root, as well as y.

`(4x√(3x) )/(y√(3x) )`

Rationalize

`(4x√(3x) )/(y√(3x) )*(√(3x) )/(√(3x) ) =(4x*3x)/(y*3x) =(12x^2)/(3xy)=(4x)/(y)`