Question

What number u satisfies the equation sqrt{100u-100}=100?

Answer 1

The answer is 101
100 squared is 10,000
Then form an equation
100u-100=10,000
        +100    +100
100u=10,100
divide by 100 on both sides
and you get 101 as the answer

Answer 2

Answer:

101

Step-by-step explanation:

If $\sqrt{100u-100}=100$, then in words, $100u-100$ is the number whose square root is $100$.

The number whose square root is $100$ is $100^2$, that is, $10{,}000$.

(If that's confusing, think of what number you can replace $\textcolor{red}{\heartsuit}$ with so that the equation $\sqrt{\textcolor{red}{\heartsuit}}=100$ is true. It's true that $\sqrt{10{,}000} = 100$.)

So, we have the equation

$$100u-100=10{,}000.$$Adding $100$ to both sides gives

$$100u=10{,}100,$$then dividing both sides by $100$ gives

$$u=\boxed{101}.$$