Question

Please help me! Not too hard but i am confused!

Answer 1

`7x^(2)\sqrt{5y^(7) }`

Explanation:

First, we'll start by simplifying
`√(125)`. 2 factors of 125 are 5 and 25, and since 25 is a perfect square, that can be taken out of the radicand and added to the 2 that's already outside of it, creating
`7\sqrt{5x^(4)y^(7)}`.

x to the power of 4 can be simplified to x squared and taken out of the radicand along with that 7, so:

`7x^(2)\sqrt{5y^(7) }`

y to the power of 7 is a bit trickier to solve, so I left it like this, because I think it's the simplest version, but if this isn't an option then simplify further by working on the y.

I hope this helps :)

Answer 2

`10 √(5) \ x^2y^3√(y)`

Explanation:

simplify
`2√(125x^4y^7)`

Apply radical rule
`√(ab) =√(a) √(b)`:

`\implies 2√(125)√(x^4)√(y^7)`

`\implies 2 \cdot 5 √(5)√(x^4)√(y^7)`

`\implies 10 √(5)√(x^4)√(y^7)`

Apply radical rule
`\sqrt[n]{a^m} =a^{(m)/(n)}`:

`\implies 10 √(5) \ x^(\frac42)y^(\frac72)`

`\implies 10 √(5) \ x^2y^3√(y)`