State that how 5√2=√50?

2 Answers

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

Jun 24, 2018

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!