What is sqrt(3+2\sqrt{2)} ?

The solution to sqrt(3+2\sqrt{2)} is sqrt(2)+1

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simplify sqrt(3+2\sqrt{2)}

simplify

3 + 22

2 + 1

Decimal Notation

2.41421 \dots

Solution steps

3 + 22

= 2 + 22 + 1

= (2)^{2} + 22 + (1)^{2}

1 = 1

= (2)^{2} + 22 + 1^{2}

22 \cdot 1 = 22

= (2)^{2} + 22 \cdot 1 + 1^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(2)^{2} + 22 \cdot 1 + 1^{2} = (2 + 1)^{2}

= (2 + 1)^{2}

Apply radical rule:

(2 + 1)^{2} = 2 + 1

= 2 + 1

a^{3} + a^{2} b + a b^{2} + b^{3}

\frac{k}{3} + 8 = 2

6 a^{2} + a - 12

3 y + 6 = 2 + 2 y