What is sqrt(32-10\sqrt{7)} ?

The solution to sqrt(32-10\sqrt{7)} is 5-sqrt(7)

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simplify sqrt(32-10\sqrt{7)}

simplify

32 - 107

5 - 7

Solution steps

32 - 107

= 7 - 107 + 25

= (7)^{2} - 107 + (25)^{2}

25 = 5

= (7)^{2} - 107 + 5^{2}

27 \cdot 5 = 107

= (7)^{2} - 27 \cdot 5 + 5^{2}

Apply Perfect Square Formula:

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

(7)^{2} - 27 \cdot 5 + 5^{2} = (7 - 5)^{2}

= (7 - 5)^{2}

Apply exponent rule:

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

n

is even

(7 - 5)^{2} = (5 - 7)^{2}

= (5 - 7)^{2}

Apply radical rule:

(5 - 7)^{2} = 5 - 7

= 5 - 7

- 3 y - 2 y

4 x^{2} + 20 x - 16

\frac{1 2}{2}

1.1 \cdot 1 0^{5}

9 u^{2} - 4 v^{2}