What is the simplest form of the quotient 4 sqrt 810 / 4 sqrt 2?

Solution:

Given 4 sqrt 810 / 4 sqrt 2

It means 4(√810) / 4(√2)

This is a problem of surds

Surd is simply used to refer to a number that does not have a root.

The number 4 gets cancelled.

√810 can be written as √(81*10)= 9√10

Now, 9√10 / √2

Again √10 can be written as √2*5

We know that √ab = √a*√b

So, √10 = √2*√5

Hence 9√10 / √2 = 9 √2*√5 / √2

√2 will be cancelled.

Therefore, the result is 9√5.

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What is the simplest form of the quotient 4 sqrt 810 / 4 sqrt 2?

Summary:

The simplest form of the quotient 4 sqrt 810 / 4 sqrt 2 is 9√5.