What is (sqrt(10^6-10^4*5^2))/(sqrt(5^4-10^4)) ?

The solution to (sqrt(10^6-10^4*5^2))/(sqrt(5^4-10^4)) is -(sqrt(10^6-10^4*5^2))/(25sqrt(15))i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (sqrt(10^6-10^4*5^2))/(sqrt(5^4-10^4))

simplify

\frac{1 0 ^{6} - 1 0 ^{4} \cdot 5 ^{2}}{5 ^{4} - 1 0 ^{4}}

- \frac{1 0 ^{6} - 1 0 ^{4} \cdot 5 ^{2}}{25 15} i

Solution steps

\frac{1 0 ^{6} - 1 0 ^{4} \cdot 5 ^{2}}{5 ^{4} - 1 0 ^{4}}

5^{4} - 1 0^{4} = 2515 i

= \frac{1 0 ^{6} - 1 0 ^{4} \cdot 5 ^{2}}{25 15 i}

Multiply by the conjugate

\frac{- i}{- i}

= \frac{1 0 ^{6} - 1 0 ^{4} \cdot 5 ^{2} ( - i )}{25 15 i ( - i )}

Simplify

\frac{1 0 ^{6} - 1 0 ^{4} \cdot 5 ^{2} ( - i )}{25 15 i ( - i )} : \frac{- i 1 0 ^{6} - 1 0 ^{4} \cdot 5 ^{2}}{25 15}

= \frac{- i 1 0 ^{6} - 1 0 ^{4} \cdot 5 ^{2}}{25 15}

Rewrite in standard complex form:

- \frac{1 0 ^{6} - 1 0 ^{4} \cdot 5 ^{2}}{25 15} i

= - \frac{1 0 ^{6} - 1 0 ^{4} \cdot 5 ^{2}}{25 15} i

x y

2 \cdot 1 0^{- 7} (\frac{10}{0.07} + \frac{20}{0.02})

\frac{- 8}{- 2}

(22) \cdot 2

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

What is (sqrt(10^6-10^4*5^2))/(sqrt(5^4-10^4)) ?
The solution to (sqrt(10^6-10^4*5^2))/(sqrt(5^4-10^4)) is -(sqrt(10^6-10^4*5^2))/(25sqrt(15))i