Which sign makes the statement true? −3√63 ? −√23

To determine which sign makes the statement true, we need to compare the two expressions: (-3sqrt{63}) and (-sqrt{23}).

First, let’s approximate the values:

1. Calculate (sqrt{63}):

[

sqrt{63} approx 7.94

]

So,

[

-3sqrt{63} approx -3 times 7.94 approx -23.82

]

2. Calculate (sqrt{23}):

[

sqrt{23} approx 4.79

]

Therefore,

[

-sqrt{23} approx -4.79

]

Now, we compare (-23.82) and (-4.79):

Since (-23.82) is less than (-4.79), we can say:

[

-3sqrt{63} < -sqrt{23}

]

Thus, the correct sign to make the statement true is “<".

So, the answer is:

[

-3sqrt{63} < -sqrt{23}

]

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