What is sqrt(7+2\sqrt{12)} ?

The solution to sqrt(7+2\sqrt{12)} is sqrt(3)+2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify sqrt(7+2\sqrt{12)}

simplify

7 + 212

3 + 2

Decimal Notation

3.73205 \dots

Solution steps

7 + 212

212 = 43

= 7 + 43

= 3 + 43 + 4

= (3)^{2} + 43 + (4)^{2}

4 = 2

= (3)^{2} + 43 + 2^{2}

23 \cdot 2 = 43

= (3)^{2} + 23 \cdot 2 + 2^{2}

Apply Perfect Square Formula:

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

(3)^{2} + 23 \cdot 2 + 2^{2} = (3 + 2)^{2}

= (3 + 2)^{2}

Apply radical rule:

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

= 3 + 2

4 x y - 6 x y + 5 y - 9 x

sin^{3} (x) + cos^{2} (x) sin (x)

(- 5) - 6

2 s (s - 4)

\frac{( - 4 m ) ^{3}}{10 m ^{- 5}}