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**

For more interesting and challenging questions like this stay tuned to Mathcompt!

Make sure you checkout the latest posts on MathCompt !

√2-1