What is sqrt(20^2+10^2) ?

The solution to sqrt(20^2+10^2) is 10sqrt(5)

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simplify sqrt(20^2+10^2)

simplify

2 0^{2} + 1 0^{2}

105

Decimal Notation

22.36067 \dots

Solution steps

2 0^{2} + 1 0^{2}

2 0^{2} + 1 0^{2} = 500

= 500

Prime factorization of

500 : 2^{2} \cdot 5^{3}

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

Apply exponent rule:

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

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

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

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

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

Apply radical rule:

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

2^{2} = 2

= 2 5^{2} 5

Apply radical rule:

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

5^{2} = 5

= 2 \cdot 55

Multiply the numbers:

2 \cdot 5 = 10

= 105

y^{5} + x^{2} y^{3}

\frac{x ^{2} - 12 x + 20}{x - 10}

(x + 2)^{2} + 1

\frac{x}{4 - x ^{2}}

- (x - 4)