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

0.23606 \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

\frac{\frac{3}{4}}{4}

x^{2} - 20 = x

4 (2 x^{2} + 1) - 2 (4 x - 1) = 2 (2 x - 1)^{2}

x^{3} - 8 x^{2} + 15 x

\frac{3}{2} + (- \frac{6}{5})