What is sqrt(30^2+30^2) ?

The solution to sqrt(30^2+30^2) is 30sqrt(2)

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simplify sqrt(30^2+30^2)

simplify

3 0^{2} + 3 0^{2}

302

Solution steps

3 0^{2} + 3 0^{2}

3 0^{2} + 3 0^{2} = 1800

= 1800

Prime factorization of

1800 : 2^{3} \cdot 3^{2} \cdot 5^{2}

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

Apply exponent rule:

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

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

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

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

= 2^{2} 2 3^{2} 5^{2}

Apply radical rule:

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

2^{2} = 2

= 22 3^{2} 5^{2}

Apply radical rule:

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

3^{2} = 3

= 22 \cdot 3 5^{2}

Apply radical rule:

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

5^{2} = 5

= 22 \cdot 3 \cdot 5

Multiply the numbers:

2 \cdot 3 \cdot 5 = 30

= 302

m^{2} - 10 m + 21

\frac{2}{3} \div \frac{2}{9}

- 2 q (4 k - 7)

3 i \cdot i

(1 + x + x^{2})^{2}