What is sqrt(6+\sqrt{20)} ?

The solution to sqrt(6+\sqrt{20)} is sqrt(5)+1

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simplify sqrt(6+\sqrt{20)}

simplify

6 + 20

5 + 1

Decimal Notation

3.23606 \dots

Solution steps

6 + 20

20 = 25

= 6 + 25

= 5 + 25 + 1

= (5)^{2} + 25 + (1)^{2}

1 = 1

= (5)^{2} + 25 + 1^{2}

25 \cdot 1 = 25

= (5)^{2} + 25 \cdot 1 + 1^{2}

Apply Perfect Square Formula:

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

(5)^{2} + 25 \cdot 1 + 1^{2} = (5 + 1)^{2}

= (5 + 1)^{2}

Apply radical rule:

(5 + 1)^{2} = 5 + 1

= 5 + 1

3 (x - 5)^{2} + 2 (x - 5)

\frac{120}{36}

4^{2.2}