QuestionSimplify the radical expression: sqrt(27) =

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the radical expression $\sqrt{27}$ . . We are to use Property1 for radicals, which states that $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$ .
3. All variables represent positive numbers.

STEP 2

We need to find factors of27 that are perfect squares. The number27 can be written as $9 \times$ , where9 is a perfect square.
$\sqrt{27} = \sqrt{9 \times}$

STEP 3

Now, we apply Property1 for radicals to separate the square root of9 and the square root of3.
$\sqrt{9 \times3} = \sqrt{9} \times \sqrt{3}$

STEP 4

We calculate the square root of9, which is3.
$\sqrt{9} =3$ So,
$\sqrt{9} \times \sqrt{3} =3 \times \sqrt{3}$

STEP 5

The simplified form of $\sqrt{27}$ is $3\sqrt{3}$ .
So, $\sqrt{27} =3\sqrt{3}$ .

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QuestionSimplify the radical expression: sqrt(27) =

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the radical expression $\sqrt{27}$ . . We are to use Property1 for radicals, which states that $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$ .
3. All variables represent positive numbers.

STEP 2

We need to find factors of27 that are perfect squares. The number27 can be written as $9 \times$ , where9 is a perfect square.
$\sqrt{27} = \sqrt{9 \times}$

STEP 3

Now, we apply Property1 for radicals to separate the square root of9 and the square root of3.
$\sqrt{9 \times3} = \sqrt{9} \times \sqrt{3}$

STEP 4

We calculate the square root of9, which is3.
$\sqrt{9} =3$ So,
$\sqrt{9} \times \sqrt{3} =3 \times \sqrt{3}$

STEP 5

The simplified form of $\sqrt{27}$ is $3\sqrt{3}$ .
So, $\sqrt{27} =3\sqrt{3}$ .

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QuestionSimplify the radical expression: sqrt(27) =

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the radical expression 27\sqrt{27}27​. . We are to use Property1 for radicals, which states that ab=a⋅b\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}ab​=a​⋅b​.3. All variables represent positive numbers.

STEP 2

We need to find factors of27 that are perfect squares. The number27 can be written as 9×9 \times9×, where9 is a perfect square.27=9×\sqrt{27} = \sqrt{9 \times}27​=9×​

STEP 3

Now, we apply Property1 for radicals to separate the square root of9 and the square root of3.9×3=9×3\sqrt{9 \times3} = \sqrt{9} \times \sqrt{3}9×3​=9​×3​

STEP 4

We calculate the square root of9, which is3.9=3\sqrt{9} =39​=3So,9×3=3×3\sqrt{9} \times \sqrt{3} =3 \times \sqrt{3}9​×3​=3×3​

STEP 5

The simplified form of 27\sqrt{27}27​ is 333\sqrt{3}33​.So, 27=33\sqrt{27} =3\sqrt{3}27​=33​.

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Assumptions1. We are asked to simplify the radical expression $\sqrt{27}$ . . We are to use Property1 for radicals, which states that $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$ .
3. All variables represent positive numbers.

We need to find factors of27 that are perfect squares. The number27 can be written as $9 \times$ , where9 is a perfect square.
$\sqrt{27} = \sqrt{9 \times}$

Now, we apply Property1 for radicals to separate the square root of9 and the square root of3.
$\sqrt{9 \times3} = \sqrt{9} \times \sqrt{3}$

We calculate the square root of9, which is3.
$\sqrt{9} =3$ So,
$\sqrt{9} \times \sqrt{3} =3 \times \sqrt{3}$

The simplified form of $\sqrt{27}$ is $3\sqrt{3}$ .
So, $\sqrt{27} =3\sqrt{3}$ .