Question

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.

Answer 1

Answer:

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

Answer 2

ANSWER

$\sqrt{9} \: and \: \sqrt{16}$

EXPLANATION

First, simplify the square roots.

$\sqrt{4} = \sqrt{ {2}^{2} } = 2$

$\sqrt{9} = \sqrt{ {3}^{2} } = 3$

$\sqrt{16} = \sqrt{ {4}^{2} } = 4$

$\sqrt{25} = \sqrt{ {5}^{2} } = 5$

Let us simplify t
$\sqrt{12}$
Although 12 is not a perfect square, it contains, a perfect square.

$\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2 \sqrt{3}$

We can now observe that,

$3 \: < \: 2 \sqrt{3} \: < \: 4$

Therefore,

$\sqrt{9} \: < \: \sqrt{12} \: < \: \sqrt{16}$

Hence

$\sqrt{12}$
is between,

$\sqrt{9}$
and

$\sqrt{16}$