QuestionSimplify $\sqrt{48}$ . Options: $16 \sqrt{3}$ , 24, $4 \sqrt{2}$ , $4 \sqrt{3}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the square root of48. . We assume that all numbers are real numbers.

STEP 2

To simplify a square root, we look for perfect squares that are factors of the number under the square root. In this case, we are looking for perfect squares that are factors of48.

STEP 3

The perfect squares less than48 are1,,9,16,25, and36. Of these, the ones that are factors of48 are1,, and16.

STEP 4

We choose the largest perfect square factor, which is16. We can write48 as $16 \times3$ .

STEP 5

We substitute this into the square root.
$\sqrt{48} = \sqrt{16 \times3}$

STEP 6

We use the property of square roots that the square root of a product is the product of the square roots.
$\sqrt{16 \times3} = \sqrt{16} \times \sqrt{3}$

STEP 7

We calculate the square root of16.
$\sqrt{16} =4$

STEP 8

We substitute this back into the equation.
$\sqrt{16} \times \sqrt{3} =4 \times \sqrt{3}$ So, $\sqrt{48}$ simplifies to $4 \sqrt{3}$ .

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QuestionSimplify $\sqrt{48}$ . Options: $16 \sqrt{3}$ , 24, $4 \sqrt{2}$ , $4 \sqrt{3}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the square root of48. . We assume that all numbers are real numbers.

STEP 2

To simplify a square root, we look for perfect squares that are factors of the number under the square root. In this case, we are looking for perfect squares that are factors of48.

STEP 3

The perfect squares less than48 are1,,9,16,25, and36. Of these, the ones that are factors of48 are1,, and16.

STEP 4

We choose the largest perfect square factor, which is16. We can write48 as $16 \times3$ .

STEP 5

We substitute this into the square root.
$\sqrt{48} = \sqrt{16 \times3}$

STEP 6

We use the property of square roots that the square root of a product is the product of the square roots.
$\sqrt{16 \times3} = \sqrt{16} \times \sqrt{3}$

STEP 7

We calculate the square root of16.
$\sqrt{16} =4$

STEP 8

We substitute this back into the equation.
$\sqrt{16} \times \sqrt{3} =4 \times \sqrt{3}$ So, $\sqrt{48}$ simplifies to $4 \sqrt{3}$ .

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QuestionSimplify 48\sqrt{48}48​. Options: 16316 \sqrt{3}163​, 24, 424 \sqrt{2}42​, 434 \sqrt{3}43​.

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the square root of48. . We assume that all numbers are real numbers.

STEP 2

To simplify a square root, we look for perfect squares that are factors of the number under the square root. In this case, we are looking for perfect squares that are factors of48.

STEP 3

The perfect squares less than48 are1,,9,16,25, and36. Of these, the ones that are factors of48 are1,, and16.

STEP 4

We choose the largest perfect square factor, which is16. We can write48 as 16×316 \times316×3.

STEP 5

We substitute this into the square root.48=16×3\sqrt{48} = \sqrt{16 \times3}48​=16×3​

STEP 6

We use the property of square roots that the square root of a product is the product of the square roots.16×3=16×3\sqrt{16 \times3} = \sqrt{16} \times \sqrt{3}16×3​=16​×3​

STEP 7

We calculate the square root of16.16=4\sqrt{16} =416​=4

STEP 8

We substitute this back into the equation.16×3=4×3\sqrt{16} \times \sqrt{3} =4 \times \sqrt{3}16​×3​=4×3​So, 48\sqrt{48}48​ simplifies to 434 \sqrt{3}43​.

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QuestionSimplify $\sqrt{48}$ . Options: $16 \sqrt{3}$ , 24, $4 \sqrt{2}$ , $4 \sqrt{3}$ .

We choose the largest perfect square factor, which is16. We can write48 as $16 \times3$ .

We substitute this into the square root.
$\sqrt{48} = \sqrt{16 \times3}$

We use the property of square roots that the square root of a product is the product of the square roots.
$\sqrt{16 \times3} = \sqrt{16} \times \sqrt{3}$

We calculate the square root of16.
$\sqrt{16} =4$

We substitute this back into the equation.
$\sqrt{16} \times \sqrt{3} =4 \times \sqrt{3}$ So, $\sqrt{48}$ simplifies to $4 \sqrt{3}$ .