Question

Simplify sqrt(3 + 2 sqrt 2) ...?

Answer 1

The answer is 1 + √2

sqrt(2) is $\sqrt{2}$
sqrt(3 + 2 sqrt 2) is $\sqrt{3 +2 \sqrt{2} }$
Now, let's simplify $\sqrt{3 +2 \sqrt{2} }$.
We will use square of sum: (a + b)² = a² + 2ab + b²

$\sqrt{3 +2 \sqrt{2} } = \sqrt{1+2+2 \sqrt{2} }= \sqrt{1+2 \sqrt{2}+2 }= \\ = \sqrt{1^{2} +2*1* \sqrt{2} + (\sqrt{2} ) ^{2} } = \sqrt{(1+ \sqrt{2}) ^{2}} =1+ \sqrt{2}$

Answer 2

Answer:

$1+\sqrt{2}$

Step-by-step explanation:

We have been given a radical expression $\sqrt{3+2\sqrt{2}}$. We are asked to simplify the given expression.

We will add $(\sqrt{2})^2-2$ to our given expression as after adding and subtracting same quantity the value of our expression will be same.

$\sqrt{3+2\sqrt{2}+(\sqrt{2})^2-2}$

$\sqrt{3-2+2\sqrt{2}+(\sqrt{2})^2}$

$\sqrt{1+2\sqrt{2}+(\sqrt{2})^2}$

Using perfect square formula $(a+b)^2=a^2+2ab+b^2$ we can rewrite our expression as:

$\sqrt{1^2+2\sqrt{2}\cdot 1+(\sqrt{2})^2}$

$\sqrt{(1+\sqrt{2})^2}$

Applying radical rule $\sqrt[n]{x^n} =x$, we will get,

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

Therefore, the simplified form of our given expression would be $1+\sqrt{2}$.