Which expression can be simplified to the form - id315376385, miraclejones543

Ответ:

GhostBoooty

12.04.2022

Mathematics

Choice B) $\sqrt{63}$

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Explanation:

Let's rewrite the given expression like so

$3\sqrt{y+3}=\sqrt{3^2}\sqrt{y+3}\\\\3\sqrt{y+3}=\sqrt{9}\sqrt{y+3}\\\\3\sqrt{y+3}=\sqrt{9(y+3)}\\\\$

We can see that the radicand is a multiple of 9 since 9 is a factor.

This immediately rules out choices C and D because 75 and 84 are not multiples of 9.

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Plug in the smallest positive integer (1) for y to get

$\sqrt{9(1+3)}=\sqrt{9(4)} = \sqrt{36}\\\\$

The radicand 36 is larger than the radicand for choice A (18), meaning we can rule out choice A. There's no way to get a radicand of 18 since y = 1 is the smallest we can go for.

We can however get to 63 by using y = 4

$\sqrt{9(4+3)}=\sqrt{9(7)} = \sqrt{63}\\\\$

Showing that choice B is of the form $3\sqrt{y+3}$ where y is a positive integer, specifically when y = 4.

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Which expression can be simplified to the form 3\y + 3, where y is a positive integer?

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