What is sqrt(45^2+90^2) ?

The solution to sqrt(45^2+90^2) is 45sqrt(5)

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simplify sqrt(45^2+90^2)

simplify

4 5^{2} + 9 0^{2}

455

Decimal Notation

100.62305 \dots

Solution steps

4 5^{2} + 9 0^{2}

4 5^{2} + 9 0^{2} = 10125

= 10125

Prime factorization of

10125 : 3^{4} \cdot 5^{3}

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

Apply exponent rule:

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

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

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

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

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

3^{4} = 9

= 9 5^{2} 5

Apply radical rule:

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

5^{2} = 5

= 9 \cdot 55

Multiply the numbers:

9 \cdot 5 = 45

= 455

\frac{9 - 10 i}{9 + i}

x^{4} - 13 x^{2} + 36

- 0.5 (0.7 q - 0.9) + 2 q

1 \times i

\frac{5}{6} \times 2