What is sqrt(11+6\sqrt{2)} ?

The solution to sqrt(11+6\sqrt{2)} is sqrt(2)+3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify sqrt(11+6\sqrt{2)}

simplify

11 + 62

2 + 3

Decimal Notation

4.41421 \dots

Solution steps

11 + 62

= 2 + 62 + 9

= (2)^{2} + 62 + (9)^{2}

9 = 3

= (2)^{2} + 62 + 3^{2}

22 \cdot 3 = 62

= (2)^{2} + 22 \cdot 3 + 3^{2}

Apply Perfect Square Formula:

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

(2)^{2} + 22 \cdot 3 + 3^{2} = (2 + 3)^{2}

= (2 + 3)^{2}

Apply radical rule:

(2 + 3)^{2} = 2 + 3

= 2 + 3

(3 x + 4) (4 x - 3)

cos^{2} (2 θ) - sin^{2} (2 θ)

(- 6 - 3 i) - (12 + 10 i)

\frac{33}{54}

2 x^{3} - x^{2} - 6 x