Remove all perfect squares from inside the square root assume y is positive ✔️200y^4

1 answer:

kondor19780726 [428]3 years ago

7 0

$\bf \sqrt{200y^4}\qquad 
\begin{cases}
200=2\cdot 2\cdot 2\cdot 5\cdot 5\\
\qquad 2^2\cdot 2\cdot 5^2\\
y^4=y^{2+2}\\
\qquad y^2\cdot y^2\\
\qquad (y^2)^2
\end{cases}\implies \sqrt[2]{2^2\cdot 2\cdot 5^2\cdot (y^2)^2}
\\\\\\
2\cdot 5\cdot y^2\sqrt{2}\implies 10y^2\sqrt{2}$

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Step-by-step explanation:

Notice that there are two unknowns in this problem: 1) the amount of solution A that is being used, and 2) the amount of solution B being used. We can name such unknowns with letters to facilitate our work:

Amount of solution A to be used = A

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So, since we need to find two unknowns, we need to create a system of two equations to solve them.

Our first equation can be obtained from the sentence: "She uses twice as much Solution A as Solution B," which written in mathematical form is:

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Now we can use our first equation to substitute A in terms of B in the second equation:

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