Question

$\large\red{\sf{Question}}$
Simplify the following
$\large\pink{\sf{ \sqrt{7 - 2\sqrt{6} } }}$
​

Answer 1

Answer:

2

Given :

bullet sqrt 7+2 sqrt 6 - sqrt 7-2 sqrt 6

To Find:

• Calculate the value.

Required Solution :

Let's start solving the problem and understand the steps to get our final result.

: Rightarrow sqrt 7+2 sqrt 6 - sqrt 7-2 sqrt 6

Simplify the expression by arranging the expression in the radical sign,

: Rightarrow1+ sqrt 6 - sqrt 7-2 sqrt 6

Simplify the expression by arranging theexpression in the radical sign,

: Rightarrow1+ sqrt 6 -(-1+6)

Change the symbol of each term in parentheses when there is a (-) symbol front of parentheses,

: Rightarrow1+ sqrt 6 +1- sqrt 6

Remove the two numbers if the values are the same and the signs are different

: Rightarrow1+1

Add 1 and 1,

: Rightarrow boxed 2

Hence Solved!

Answer is = 2

please give me brain list and thanks

Answer 2

$\large\underline{\sf{Solution-}}$

Given expression is

$\sqrt{7 - 2 \sqrt{6} }$

can be rewritten as

$= \sqrt{6 + 1 - 2 \sqrt{6} }$

$= \sqrt{ {( \sqrt{6} )}^{2} + {(1)}^{2} - 2 \sqrt{6} }$

$= \sqrt{ {( \sqrt{6} )}^{2} + {(1)}^{2} - 2 \times \sqrt{6} \times 1 }$

We know,

$\boxed{ \rm{ \: {x}^{2} + {y}^{2} - 2xy = {(x - y)}^{2} \: }}$

Here,

$x = \sqrt{6}$

$y = 1$

So, using above identity, we get

$= \sqrt{ {( \sqrt{6} - 1) }^{2} }$

$= \sqrt{6} - 1$

Hence,

$\rm\implies \:\boxed{ \rm{ \: \sqrt{7 - 2 \sqrt{6} } = \sqrt{6} - 1 \: \: }}$

$\rule{190pt}{2pt}$

Additional information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: identities}}}} \\ \\ \bigstar \: \bf{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \bigstar \: \bf{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \bigstar \: \bf{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$