What is sqrt(7-4\sqrt{3)} ?

The solution to sqrt(7-4\sqrt{3)} is 2-sqrt(3)

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Popular >

simplify sqrt(7-4\sqrt{3)}

simplify

7 - 43

2 - 3

Decimal Notation

0.26794 \dots

Solution steps

7 - 43

= 3 - 43 + 4

= (3)^{2} - 43 + (4)^{2}

4 = 2

= (3)^{2} - 43 + 2^{2}

23 \cdot 2 = 43

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

Apply Perfect Square Formula:

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

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

= (3 - 2)^{2}

Apply exponent rule:

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

n

is even

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

= (2 - 3)^{2}

Apply radical rule:

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

= 2 - 3

(x - 2) (x - 2) (x - 2)

6^{2} + \frac{2 ( 5 - 3 )}{2} + 10 \cdot 5

4 (2)

(3 x + 5) (2 x^{2} - 2 x - 1)

(a - b)^{5}