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

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

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simplify sqrt(10^2+20^2)

simplify

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

105

Decimal Notation

22.36067 \dots

Solution steps

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

1 0^{2} + 2 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

8 x^{2} + 10 x y + 3 y^{2}

(x^{2} + 3 x - 10) \frac{6}{3 x - 6}

\frac{x - 5}{4 x + 8} \cdot (12 x^{2} + 32 x + 16)

x (2 x^{2} + 3 x y + y^{2}) - y (5 x^{2} - 2 x y + y^{2})

(7 - 5) (7 + 5)