What is sqrt(25+10\sqrt{5)+5} ?

The solution to sqrt(25+10\sqrt{5)+5} is sqrt(5)+5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify sqrt(25+10\sqrt{5)+5}

simplify

25 + 105 + 5

5 + 5

Decimal

7.23606 \dots

Solution steps

25 + 105 + 5

Add the numbers:

25 + 5 = 30

= 30 + 105

= 5 + 105 + 25

= (5)^{2} + 105 + (25)^{2}

25 = 5

= (5)^{2} + 105 + 5^{2}

25 \cdot 5 = 105

= (5)^{2} + 25 \cdot 5 + 5^{2}

Apply Perfect Square Formula:

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

(5)^{2} + 25 \cdot 5 + 5^{2} = (5 + 5)^{2}

= (5 + 5)^{2}

Apply radical rule:

n a^{n} = a

(5 + 5)^{2} = 5 + 5

= 5 + 5

\frac{5}{5 x + 2} \geq 0

\frac{5}{7} - \frac{1}{2}

\frac{1}{2} 12 \cdot 8

\frac{x ^{- 1} + y ^{- 1}}{z ^{- 1}}

y^{4} - 5 y^{2} + 4

What is sqrt(25+10\sqrt{5)+5} ?
The solution to sqrt(25+10\sqrt{5)+5} is sqrt(5)+5