What is sqrt(9+4\sqrt{2)} ?

The solution to sqrt(9+4\sqrt{2)} is 2sqrt(2)+1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify sqrt(9+4\sqrt{2)}

simplify

9 + 42

22 + 1

Decimal Notation

3.82842 \dots

Solution steps

9 + 42

= 8 + 42 + 1

= 4 \cdot 2 + 42 + 1

= (4)^{2} (2)^{2} + 42 + (1)^{2}

4 = 2

1 = 1

= 2^{2} (2)^{2} + 42 + 1^{2}

2 \cdot 22 \cdot 1 = 42

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

Apply Perfect Square Formula:

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

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

= (22 + 1)^{2}

Apply radical rule:

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

= 22 + 1

\frac{5 - 10 i}{9 + 6 i}

\frac{7}{8} o f^{1000}

- 2 x^{2} + 12 x - 16

(\times (- 2))^{2}

\frac{128}{15}