Hey guys! Today is a challenge for you. Can you solve this Cambridge interview question??

## The “Cambridge” Question

So guys, here’s the question

#### Solve: √(3−2√2)

Yes this question has been asked in Cambridge Interview.

Take your time ! First do it yourself and don’t see the solution below.

### The Solution

You probably heard of a mathematical identity that seems like this :

( A – B )² = A² – 2.A.B + B²

Can you now relate something ?

We have to make 3 – 2√2 in the form of above identity which means 3 – 2√2 is a perfect square. Let’s start with the above identity:

( A – B )² = A² – 2.A.B + B²

If we relate (- 2) in the question and (- 2) in the identity, we can consider √2 as either A or B ( after considering √2 as A )

( √2 – B )² = (√2)² – 2.(√2).B + B²

Now we can simplify 3 in the question as 3 = 2+1 so taking B as 1,

( √2 – 1 )² = (√2)² – 2.(√2).1 + (1)²

3 – 2√2 = ( √2 – 1 )² = (√2)² – 2.(√2).1 + (1)²

Hooray! here’s is our perfect square. Now if we put the value of 3-2√2 i.e, (√2 – 1 )² in the question, it becomes

√(3 – 2√2) = √ ((√2 – 1 )²)

➡√ ((√2 – 1 )²) = √2 – 1

√(3−2√2) = √2 – 1

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