Question

State that how 5√2=√50?

Answer 1

By the law of surds:
`sqrta sqrtb = sqrt(ab)`

Explanation:

This style question is that of surds.

We know `sqrta sqrtb = sqrt(ab)`

So in the form `sqrta sqrt2 = sqrt50`

We need to find what a is
By rearranging the question we can find
`sqrta = sqrt50/sqrt2`

To get a on its own we square both sides of the equations to give;
`a = 50/2`

Therefore `a = 25`

Therefore `sqrt50 = sqrt25sqrt2`
Furthermore to simplify `sqrt25 = 5`

Answer 2

See below:

Explanation:

Let's start with `sqrt50`. Because of the radical law

`sqrt(ab)=sqrta*sqrtb`

We can rewrite `sqrt50` as the product of two square roots.

We know `50=25*2`, and writing it this way allows us to simplify the radical:

`sqrt(25*2)=color(steelblue)(sqrt25)*sqrt2`

What I have in blue can be simplified, and we're left with

`color(steelblue)(5sqrt2)`

We were able to do this because `sqrt50` and `sqrt(25*2)` are saying the same thing. Writing it in the latter way allows us to factor out a perfect square.

Hope this helps!