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

0.23606 \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

16 x^{3} + 16 x^{2} - 9 x - 9

8 y^{2} + 7 x y - 2 y^{2} - 5 x y + 2 x

\frac{4}{30} + \frac{1}{20}

x^{2} y - y - zy

x^{4} (- 2 x)^{3} (6 x^{0})^{- 2}