What is sqrt(7-2\sqrt{12)} ?

The solution to sqrt(7-2\sqrt{12)} is 2-sqrt(3)

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Popular >

simplify sqrt(7-2\sqrt{12)}

simplify

7 - 212

2 - 3

Decimal Notation

0.26794 \dots

Solution steps

7 - 212

212 = 43

= 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

∣ - 17 ∣

4 x 192 - 3 x^{2}

12 x^{3} + 8 x^{2} - x - 1

(h + 2)^{2}

0.2 5^{10}