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

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

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simplify sqrt(1^2+(-\sqrt{3))}^2

simplify

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

1 - 3

Decimal Notation

- 0.73205 \dots

Solution steps

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

Apply radical rule:

a = a^{\frac{1}{2}}

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}

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

\frac{1}{2} \cdot 2 = 1

= (1^{2} + (- 3))

Apply rule

1^{a} = 1

1^{2} = 1

= 1 - 3

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