What is sqrt(30+10\sqrt{5)} ?

The solution to sqrt(30+10\sqrt{5)} is sqrt(5)+5

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simplify sqrt(30+10\sqrt{5)}

simplify

30 + 105

5 + 5

Decimal Notation

7.23606 \dots

Solution steps

30 + 105

= 5 + 105 + 25

= (5)^{2} + 105 + (25)^{2}

25 = 5

= (5)^{2} + 105 + 5^{2}

25 \cdot 5 = 105

= (5)^{2} + 25 \cdot 5 + 5^{2}

Apply Perfect Square Formula:

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

(5)^{2} + 25 \cdot 5 + 5^{2} = (5 + 5)^{2}

= (5 + 5)^{2}

Apply radical rule:

(5 + 5)^{2} = 5 + 5

= 5 + 5

x^{2} - 24 x + 108

∣ x (x + 4) ∣ > x

u^{2} + 4 u + 4

5 - \frac{x}{3} = \frac{3 ( x + 1 )}{7}