State that how 5√2=√50?

2 Answers
Marksyboy16 · Jacobi J.
Jun 24, 2018

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#

Jacobi J.
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!

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