What is (3-5sqrt(3))^2 ?

The solution to (3-5sqrt(3))^2 is 84-30sqrt(3)

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simplify (3-5sqrt(3))^2

simplify

(3 - 53)^{2}

84 - 303

Decimal Notation

32.03847 \dots

Solution steps

(3 - 53)^{2}

Apply Perfect Square Formula:

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

(3 - 53)^{2} = 3^{2} - 2 \cdot 3 \cdot 53 + (53)^{2}

= 3^{2} - 2 \cdot 3 \cdot 53 + (53)^{2}

3^{2} - 2 \cdot 3 \cdot 53 + (53)^{2} = 84 - 303

= 84 - 303

\frac{3 x ^{- \frac{1}{2}} \cdot 3 x ^{\frac{1}{2}} y ^{- \frac{1}{3}}}{3 y ^{- \frac{7}{4}}}

500 \leq \frac{( x + 1 ) ^{2}}{4} \leq 1000

x^{3} + 4 x^{2} + 4 x + 16

\frac{x}{7} + 4 = - 5

2.2 m < 11