What is sqrt((1-\sqrt{10))}^2 ?

The solution to sqrt((1-\sqrt{10))}^2 is 1-sqrt(10)

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simplify sqrt((1-\sqrt{10))}^2

simplify

(1 - 10)^{2}

1 - 10

Decimal Notation

- 2.16227 \dots

Solution steps

(1 - 10)^{2}

Apply rule:

(a) = a

(1 - 10) = 1 - 10

= (1 - 10)^{2}

1 - 10 = - 1 + 10 i

= (- 1 + 10 i)^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(- 1 + 10 i)^{2} = (- 1 + 10)^{2} i^{2}

= (- 1 + 10)^{2} i^{2}

Apply exponent rule:

(- 1 + 10)^{2} = - 1 + 10

= (- 1 + 10) i^{2}

Apply imaginary number rule:

i^{2} = - 1

= (- 1 + 10) (- 1)

Apply rule:

a (- b) = - ab

(- 1 + 10) (- 1) = - (- 1 + 10) \cdot 1

= - (- 1 + 10) \cdot 1

Apply rule:

a \cdot 1 = a

= - (- 1 + 10)

Apply the distributive law:

- (- a + b) = a - b

- (- 1 + 10) = 1 - 10

= 1 - 10

9.34 \cdot 1 0^{- 5}

e^{- \frac{6}{8}}

(2 \cdot 1 0^{- 8}) \cdot (1.5 \cdot 1 0^{12})

e^{- 0^{3}}

What is sqrt((1-\sqrt{10))}^2 ?
The solution to sqrt((1-\sqrt{10))}^2 is 1-sqrt(10)