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

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

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

simplify

14 - 65

3 - 5

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 exponent rule:

(- a)^{n} = a^{n},

n

is even

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

= (3 - 5)^{2}

Apply radical rule:

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

= 3 - 5

\frac{x - 1}{x + 2}

(- 3 - 2 i) - (- 5 + i)

\frac{x ^{2} + 2 x - 15}{x ^{2} - x - 6}

\frac{2 x ^{- 1}}{y ^{- 1} - 2 x ^{- 1}}

(4 x) (4 x)