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

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

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simplify sqrt(50^2+50^2)

simplify

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

502

Decimal Notation

70.71067 \dots

Solution steps

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

5 0^{2} + 5 0^{2} = 5000

= 5000

Prime factorization of

5000 : 2^{3} \cdot 5^{4}

= 2^{3} \cdot 5^{4}

Apply exponent rule:

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

2^{3} \cdot 5^{4} = 2^{2} \cdot 2 \cdot 5^{4}

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

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

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

Apply radical rule:

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

2^{2} = 2

= 22 5^{4}

5^{4} = 25

= 22 \cdot 25

Multiply the numbers:

2 \cdot 25 = 50

= 502

\frac{a ^{n}}{a ^{m}}

(160 x^{7})^{\frac{1}{4}}

cos (t) tan (t)

π 1 2^{2}

(4 x - 3 y)^{6}