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

Decimal Notation

1.23606 \dots

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

(i^{2} + 3) - (7 + i^{3})

(- 7 x^{2} + 5 x + 10) - (- 10 x + 3)

\frac{y ^{5} - 5 y ^{3} + 2 y}{y ^{- 3}}

\frac{2 ( r ) ^{2}}{6 r ^{5}}