What is sqrt(27-10\sqrt{2)} ?

The solution to sqrt(27-10\sqrt{2)} is 5-sqrt(2)

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simplify sqrt(27-10\sqrt{2)}

simplify

27 - 102

5 - 2

Decimal Notation

3.58578 \dots

Solution steps

27 - 102

= 2 - 102 + 25

= (2)^{2} - 102 + (25)^{2}

25 = 5

= (2)^{2} - 102 + 5^{2}

22 \cdot 5 = 102

= (2)^{2} - 22 \cdot 5 + 5^{2}

Apply Perfect Square Formula:

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

(2)^{2} - 22 \cdot 5 + 5^{2} = (2 - 5)^{2}

= (2 - 5)^{2}

Apply exponent rule:

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

n

is even

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

= (5 - 2)^{2}

Apply radical rule:

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

= 5 - 2

(3 + h)^{- 1} - 3^{- 1}

\frac{16}{70}

(x + \frac{3}{5})^{3}

(- 8 x^{2} - 9) - (- 5 x^{2} + 5 x)

- 20 - (- 4)