What is sqrt(3+8\sqrt{7+4\sqrt{3)}} ?

The solution to sqrt(3+8\sqrt{7+4\sqrt{3)}} is sqrt(3)+4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify sqrt(3+8\sqrt{7+4\sqrt{3)}}

simplify

3 + 8 7 + 43

3 + 4

Decimal Notation

5.73205 \dots

Solution steps

3 + 8 7 + 43

3 + 8 7 + 43 = 19 + 83

= 19 + 83

= 3 + 83 + 16

= (3)^{2} + 83 + (16)^{2}

16 = 4

= (3)^{2} + 83 + 4^{2}

23 \cdot 4 = 83

= (3)^{2} + 23 \cdot 4 + 4^{2}

Apply Perfect Square Formula:

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

(3)^{2} + 23 \cdot 4 + 4^{2} = (3 + 4)^{2}

= (3 + 4)^{2}

Apply radical rule:

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

= 3 + 4

m^{2} - n^{2} - 3 mn - 5 m^{2} - n^{2} + 6 mn

75 q^{3}

- 3 + \frac{5}{2}

\frac{3}{8} \cdot \frac{5}{6}

cos (θ) (sec (θ) - cos (θ))

What is sqrt(3+8\sqrt{7+4\sqrt{3)}} ?
The solution to sqrt(3+8\sqrt{7+4\sqrt{3)}} is sqrt(3)+4