What is sqrt(9+4\sqrt{5)} ?

The solution to sqrt(9+4\sqrt{5)} is sqrt(5)+2

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Popular >

simplify sqrt(9+4\sqrt{5)}

simplify

9 + 45

5 + 2

Decimal Notation

4.23606 \dots

Solution steps

9 + 45

= 5 + 45 + 4

= (5)^{2} + 45 + (4)^{2}

4 = 2

= (5)^{2} + 45 + 2^{2}

25 \cdot 2 = 45

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

Apply Perfect Square Formula:

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

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

= (5 + 2)^{2}

Apply radical rule:

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

= 5 + 2

5 \frac{1}{5} - 16

x^{- 10}

6 \frac{3}{8}

(5 - 3 i) + (- 4 - 7 i)

6 \div \frac{2}{5}