What is sqrt(9+2\sqrt{20)} ?

The solution to sqrt(9+2\sqrt{20)} is sqrt(5)+2

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simplify sqrt(9+2\sqrt{20)}

simplify

9 + 220

5 + 2

Decimal Notation

4.23606 \dots

Solution steps

9 + 220

220 = 45

= 9 + 45

= 5 + 45 + 4

= (5)^{2} + 45 + (4)^{2}

4 = 2

= (5)^{2} + 45 + 2^{2}

25 \cdot 2 = 45

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

Apply Perfect Square Formula:

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

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

= (5 + 2)^{2}

Apply radical rule:

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

= 5 + 2

\frac{3}{( - \frac{1}{x} ) ^{2} - 2}

- 4 f - 6 (6 f - 10)

(x + 1) (2 x^{2} - x + 1)

16.5 - 2 (5.1 x + 9)

3 x - [4 - 2 x + (x - 9) + 7 x]