What is sqrt(100^2+50^2) ?

The solution to sqrt(100^2+50^2) is 50sqrt(5)

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simplify sqrt(100^2+50^2)

simplify

10 0^{2} + 5 0^{2}

505

Decimal Notation

111.80339 \dots

Solution steps

10 0^{2} + 5 0^{2}

10 0^{2} + 5 0^{2} = 12500

= 12500

Prime factorization of

12500 : 2^{2} \cdot 5^{5}

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

Apply exponent rule:

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

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

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

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

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

Apply radical rule:

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

2^{2} = 2

= 2 5^{4} 5

5^{4} = 25

= 2 \cdot 255

Multiply the numbers:

2 \cdot 25 = 50

= 505

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π \cdot \frac{π}{2}