What is sqrt((3-\sqrt{10))^2} ?

The solution to sqrt((3-\sqrt{10))^2} is sqrt(10)-3

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simplify sqrt((3-\sqrt{10))^2}

simplify

(3 - 10)^{2}

10 - 3

Decimal Notation

0.16227 \dots

Solution steps

(3 - 10)^{2}

(3 - 10)^{2} = 19 - 610

= 19 - 610

= 10 - 610 + 9

= (10)^{2} - 610 + (9)^{2}

9 = 3

= (10)^{2} - 610 + 3^{2}

210 \cdot 3 = 610

= (10)^{2} - 210 \cdot 3 + 3^{2}

Apply Perfect Square Formula:

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

(10)^{2} - 210 \cdot 3 + 3^{2} = (10 - 3)^{2}

= (10 - 3)^{2}

Apply radical rule:

(10 - 3)^{2} = 10 - 3

= 10 - 3

x^{3} \cdot x^{- 3}

3 \cdot 3

3 \cdot 2

\frac{80}{1000}

1 5^{2} + 1 0^{2}

What is sqrt((3-\sqrt{10))^2} ?
The solution to sqrt((3-\sqrt{10))^2} is sqrt(10)-3