What is sqrt(6+2\sqrt{5)} ?

The solution to sqrt(6+2\sqrt{5)} is sqrt(5)+1

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simplify sqrt(6+2\sqrt{5)}

simplify

6 + 25

5 + 1

Solution steps

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

\frac{- 0.1 + 6 - 6}{- 0.1}

\frac{15}{9} \div \frac{5}{3}

\frac{5 b - 5}{5} \cdot \frac{6}{b - 1}

5 \frac{π}{4}

8^{0} \cdot (- 4)^{2}