Question

find the value of
$\sqrt{3 - 2 \sqrt{2} }$
​

Answer 1

Answer:

$\large\boxed{\sqrt{2}-1=0.41 }$

Step-by-step explanation:

To solve this problem, first you have to solve with square root from left to right.

Given:

√3-2√2

Solutions:

First, you have to use the factors of 3-2√2.

Add and subtract numbers from left to right.

$\displaystyle\sqrt{2}^2=2$

$\displaystyle 3-2\sqrt{2}+\sqrt{2}^2-2$

Solve. (refine.)

$\displaystyle \sqrt{2}^2-2\sqrt{2}+1$

Rewrite the whole problem down.

$\displaystyle \sqrt{2}^2-2\sqrt{2}+1=\sqrt{2}^2-2\sqrt{2}*1+1^2$

Using perfect square formula.

$\large\boxed{\textnormal{Perfect Square Formula}}}$

$\displaystyle (a-b)^2=a^2-2ab+b^2$

A=√2

B=1

$\displaystyle (\sqrt{2}-1)^2$

Solve.

$\large\boxed{\textnormal{Radical Rule}}$

$\displaystyle \sqrt[n]{a^n}=a\quad a\geq0$

$\large\boxed{\sqrt{2}-1=0.41 }$

The correct answer is √2-1=0.41.

Answer 2

AnswEr :

See Here is a Rule to Break this Equation :

$\tt{ \sqrt{a + 2 \sqrt{b} } }$

We Will Break this in Two Numbers (x and y) Such that :

• a = x + y

• b = x × y

† So Let's Head to the Question :

$\leadsto \tt{ \sqrt{3 - 2 \sqrt{2} } }$

• 3 = 2 + 1
• 2 = 2 × 1

$\leadsto \tt{ \sqrt{2} - \sqrt{1} }$

• We Will Use (-) Sign Between them as there is Negative Sign in Question.

$\green{ \huge \leadsto \tt{\sqrt{2} -1}}$

$\huge{\red{\ddot{\smile}}}$