QuestionSimplify $\sqrt{12}$ to the form $a \sqrt{b}$ . What is the result?

Studdy Solution

STEP 1

Assumptions1. We are simplifying the square root of12. . The simplified form should be in the form of $a \sqrt{b}$ , where $a$ and $b$ are integers.

STEP 2

First, we need to factorize the number under the square root, which is12 in this case. The prime factorization of12 is $2^2 \times$ .
$12 =2^2 \times$

STEP 3

Now, we can rewrite the square root of12 using its prime factors.
$\sqrt{12} = \sqrt{2^2 \times3}$

STEP 4

Next, we can use the property of square roots that says the square root of a product is the product of the square roots.
$\sqrt{2^2 \times3} = \sqrt{2^2} \times \sqrt{3}$

STEP 5

Now, we can simplify $\sqrt{2^2}$ , which is2.
$\sqrt{2^2} \times \sqrt{3} =2 \sqrt{3}$ So, $\sqrt{12}$ simplifies to $2 \sqrt{3}$ .

Was this helpful?

QuestionSimplify $\sqrt{12}$ to the form $a \sqrt{b}$ . What is the result?

Studdy Solution

STEP 1

Assumptions1. We are simplifying the square root of12. . The simplified form should be in the form of $a \sqrt{b}$ , where $a$ and $b$ are integers.

STEP 2

First, we need to factorize the number under the square root, which is12 in this case. The prime factorization of12 is $2^2 \times$ .
$12 =2^2 \times$

STEP 3

Now, we can rewrite the square root of12 using its prime factors.
$\sqrt{12} = \sqrt{2^2 \times3}$

STEP 4

Next, we can use the property of square roots that says the square root of a product is the product of the square roots.
$\sqrt{2^2 \times3} = \sqrt{2^2} \times \sqrt{3}$

STEP 5

Now, we can simplify $\sqrt{2^2}$ , which is2.
$\sqrt{2^2} \times \sqrt{3} =2 \sqrt{3}$ So, $\sqrt{12}$ simplifies to $2 \sqrt{3}$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSimplify 12\sqrt{12}12​ to the form aba \sqrt{b}ab​. What is the result?

Studdy Solution

STEP 1

Assumptions1. We are simplifying the square root of12. . The simplified form should be in the form of aba \sqrt{b}ab​, where aaa and bbb are integers.

STEP 2

First, we need to factorize the number under the square root, which is12 in this case. The prime factorization of12 is 22×2^2 \times22×.12=22×12 =2^2 \times12=22×

STEP 3

Now, we can rewrite the square root of12 using its prime factors.12=22×3\sqrt{12} = \sqrt{2^2 \times3}12​=22×3​

STEP 4

Next, we can use the property of square roots that says the square root of a product is the product of the square roots.22×3=22×3\sqrt{2^2 \times3} = \sqrt{2^2} \times \sqrt{3}22×3​=22​×3​

STEP 5

Now, we can simplify 22\sqrt{2^2}22​, which is2.22×3=23\sqrt{2^2} \times \sqrt{3} =2 \sqrt{3}22​×3​=23​So, 12\sqrt{12}12​ simplifies to 232 \sqrt{3}23​.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSimplify $\sqrt{12}$ to the form $a \sqrt{b}$ . What is the result?

Assumptions1. We are simplifying the square root of12. . The simplified form should be in the form of $a \sqrt{b}$ , where $a$ and $b$ are integers.

First, we need to factorize the number under the square root, which is12 in this case. The prime factorization of12 is $2^2 \times$ .
$12 =2^2 \times$

Now, we can rewrite the square root of12 using its prime factors.
$\sqrt{12} = \sqrt{2^2 \times3}$

Next, we can use the property of square roots that says the square root of a product is the product of the square roots.
$\sqrt{2^2 \times3} = \sqrt{2^2} \times \sqrt{3}$

Now, we can simplify $\sqrt{2^2}$ , which is2.
$\sqrt{2^2} \times \sqrt{3} =2 \sqrt{3}$ So, $\sqrt{12}$ simplifies to $2 \sqrt{3}$ .