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Which two numbers does the √12 fall between? √4 √9 √16 √25 To answer, type in the box below. To answer √4, you would type square root 4.

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Answer:

9 and 16...............................................


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ANSWER

[tex] \sqrt{9} \: and \: \sqrt{16} [/tex]

EXPLANATION

First, simplify the square roots.

[tex] \sqrt{4} = \sqrt{ {2}^{2} } = 2[/tex]

[tex] \sqrt{9} = \sqrt{ {3}^{2} } = 3[/tex]

[tex] \sqrt{16} = \sqrt{ {4}^{2} } = 4[/tex]

[tex] \sqrt{25} = \sqrt{ {5}^{2} } = 5[/tex]

Let us simplify t
[tex] \sqrt{12} [/tex]
Although 12 is not a perfect square, it contains, a perfect square.

[tex] \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2 \sqrt{3} [/tex]

We can now observe that,

[tex]3 \: < \: 2 \sqrt{3} \: < \: 4[/tex]

Therefore,

[tex] \sqrt{9} \: < \: \sqrt{12} \: < \: \sqrt{16} [/tex]

Hence

[tex] \sqrt{12} [/tex]
is between,

[tex] \sqrt{9} [/tex]
and

[tex] \sqrt{16} [/tex]

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