What is sqrt(25-10\sqrt{3)+3} ?

The solution to sqrt(25-10\sqrt{3)+3} is 5-sqrt(3)

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simplify sqrt(25-10\sqrt{3)+3}

simplify

25 - 103 + 3

5 - 3

Decimal Notation

3.26794 \dots

Solution steps

25 - 103 + 3

Add the numbers:

25 + 3 = 28

= 28 - 103

= 3 - 103 + 25

= (3)^{2} - 103 + (25)^{2}

25 = 5

= (3)^{2} - 103 + 5^{2}

23 \cdot 5 = 103

= (3)^{2} - 23 \cdot 5 + 5^{2}

Apply Perfect Square Formula:

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

(3)^{2} - 23 \cdot 5 + 5^{2} = (3 - 5)^{2}

= (3 - 5)^{2}

Apply exponent rule:

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

n

is even

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

= (5 - 3)^{2}

Apply radical rule:

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

= 5 - 3

csc^{2} (x) - cot^{2} (x)

\frac{1}{sec ( x )}

\frac{tan ( x )}{sec ( x )}

(3 + 4 i)^{6}

What is sqrt(25-10\sqrt{3)+3} ?
The solution to sqrt(25-10\sqrt{3)+3} is 5-sqrt(3)