What is sqrt(12^2+4^2) ?

The solution to sqrt(12^2+4^2) is 4sqrt(10)

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simplify sqrt(12^2+4^2)

simplify

1 2^{2} + 4^{2}

410

Decimal Notation

12.64911 \dots

Solution steps

1 2^{2} + 4^{2}

1 2^{2} + 4^{2} = 160

= 160

Prime factorization of

160 : 2^{5} \cdot 5

= 2^{5} \cdot 5

Apply exponent rule:

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

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

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

Apply radical rule:

ab = a b, a \geq 0, b \geq 0

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

= 2^{4} 2 \cdot 5

2^{4} = 4

= 4 2 \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 410

(sin (θ) - cos (θ))^{2}

D x [\frac{3 x ^{2} + 1}{2 x ^{2}}]

(cos (x))^{2} + (sin (x))^{2}

2000 \cdot (1.00175)^{(12 \cdot 5)}

\frac{1}{2} x - x