What is sqrt(20^2+30^2) ?

The solution to sqrt(20^2+30^2) is 10sqrt(13)

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simplify sqrt(20^2+30^2)

simplify

2 0^{2} + 3 0^{2}

1013

Solution steps

2 0^{2} + 3 0^{2}

2 0^{2} + 3 0^{2} = 1300

= 1300

Prime factorization of

1300 : 2^{2} \cdot 5^{2} \cdot 13

= 2^{2} \cdot 5^{2} \cdot 13

2^{2} \cdot 5^{2} \cdot 13 = 2^{2} 5^{2} 13

= 2^{2} 5^{2} 13

Apply radical rule:

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

2^{2} = 2

= 2 5^{2} 13

Apply radical rule:

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

5^{2} = 5

= 2 \cdot 513

Multiply the numbers:

2 \cdot 5 = 10

= 1013

(1)^{\frac{1}{3}}

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