What is expand (1+sqrt(3))^{-2} ?

The solution to expand (1+sqrt(3))^{-2} is (2-sqrt(3))/2

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expand (1+sqrt(3))^{-2}

expand

(1 + 3)^{- 2}

\frac{2 - 3}{2}

Decimal Notation

0.13397 \dots

Solution steps

(1 + 3)^{- 2}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{( 1 + 3 ) ^{2}}

(1 + 3)^{2} = 4 + 23

= \frac{1}{4 + 2 3}

Rationalize

\frac{1}{4 + 2 3} : \frac{2 - 3}{2}

= \frac{2 - 3}{2}

(5 a^{3} b^{2} c) (4 a b^{4} c^{5})

(7 r^{3}) (9 r^{4})

e^{- 0.014984}

140000 (1 + 0.04)^{- 2 \cdot 1}

90.9 x 1 0^{- 3}

What is expand (1+sqrt(3))^{-2} ?
The solution to expand (1+sqrt(3))^{-2} is (2-sqrt(3))/2