What is sqrt(14+6\sqrt{5)} ?

The solution to sqrt(14+6\sqrt{5)} is sqrt(5)+3

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simplify sqrt(14+6\sqrt{5)}

simplify

14 + 65

5 + 3

Solution steps

14 + 65

= 5 + 65 + 9

= (5)^{2} + 65 + (9)^{2}

9 = 3

= (5)^{2} + 65 + 3^{2}

25 \cdot 3 = 65

= (5)^{2} + 25 \cdot 3 + 3^{2}

Apply Perfect Square Formula:

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

(5)^{2} + 25 \cdot 3 + 3^{2} = (5 + 3)^{2}

= (5 + 3)^{2}

Apply radical rule:

(5 + 3)^{2} = 5 + 3

= 5 + 3

y^{2} + 5 y + 4

\frac{60}{18}

(p + 5) (p + 3)

1 \frac{1}{2} \div \frac{3}{4}