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

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

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simplify sqrt(40^2+20^2)

simplify

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

205

Decimal Notation

44.72135 \dots

Solution steps

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

4 0^{2} + 2 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

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