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

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

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simplify sqrt(90^2+45^2)

simplify

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

455

Decimal Notation

100.62305 \dots

Solution steps

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

9 0^{2} + 4 5^{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

2 \times 1 0^{- 7}

\frac{2}{4} \times \frac{1}{4}

lo g_{10} (x z)

(x - 7 - i) (x - 7 + i)

s (s + 1) (s^{2} + 4 s + 5)