What is sqrt(20^2+40^2) ?

The solution to sqrt(20^2+40^2) is 20sqrt(5)

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simplify sqrt(20^2+40^2)

simplify

2 0^{2} + 4 0^{2}

205

Decimal Notation

44.72135 \dots

Solution steps

2 0^{2} + 4 0^{2}

2 0^{2} + 4 0^{2} = 2000

= 2000

Prime factorization of

2000 : 2^{4} \cdot 5^{3}

= 2^{4} \cdot 5^{3}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

2^{4} \cdot 5^{3} = 2^{4} \cdot 5^{2} \cdot 5

= 2^{4} \cdot 5^{2} \cdot 5

2^{4} \cdot 5^{2} \cdot 5 = 2^{4} 5^{2} 5

= 2^{4} 5^{2} 5

2^{4} = 4

= 4 5^{2} 5

Apply radical rule:

a^{2} = a, a \geq 0

5^{2} = 5

= 4 \cdot 55

Multiply the numbers:

4 \cdot 5 = 20

= 205

\frac{3 + i}{1 + 2 i}

1 - \frac{1}{n}

3 (a - 5)

(0.09)^{\frac{- 1}{2}}

(2 - (- 1))^{\frac{1}{2}}