Math / Numbers & Operations

QuestionExpress $12^{\frac{1}{2}}$ in simplest radical form.

Studdy Solution

STEP 1

What is this asking? We need to simplify $12^{\frac{1}{2}}$ and write it using a radical. Watch out! Remember that fractional exponents can be rewritten as radicals, and don't forget to simplify the radical completely!

STEP 2

1. Rewrite the exponent as a radical.
2. Simplify the radical.

STEP 3

Alright, let's rewrite this fractional exponent as a radical!
Remember, a fractional exponent of $\frac{1}{2}$ means we're taking the square root.
So, $12^{\frac{1}{2}}$ is the same as $\sqrt{12}$ .
It's like translating from one mathematical language to another!

STEP 4

Now, let's simplify $\sqrt{12}$ .
We're looking for the largest perfect square that divides $12$ .
That's 4, since $4 \cdot 3 = 12$ .

STEP 5

So, we can rewrite $\sqrt{12}$ as $\sqrt{4 \cdot 3}$ .
Using the product property of square roots, this becomes $\sqrt{4} \cdot \sqrt{3}$ .

STEP 6

Since $\sqrt{4} = 2$ , our expression simplifies to $2\sqrt{3}$ .
We can't simplify $\sqrt{3}$ any further, because $3$ is a prime number.

STEP 7

Our final answer is $2\sqrt{3}$ .

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QuestionExpress $12^{\frac{1}{2}}$ in simplest radical form.

Studdy Solution

STEP 1

What is this asking? We need to simplify $12^{\frac{1}{2}}$ and write it using a radical. Watch out! Remember that fractional exponents can be rewritten as radicals, and don't forget to simplify the radical completely!

STEP 2

1. Rewrite the exponent as a radical.
2. Simplify the radical.

STEP 3

Alright, let's rewrite this fractional exponent as a radical!
Remember, a fractional exponent of $\frac{1}{2}$ means we're taking the square root.
So, $12^{\frac{1}{2}}$ is the same as $\sqrt{12}$ .
It's like translating from one mathematical language to another!

STEP 4

Now, let's simplify $\sqrt{12}$ .
We're looking for the largest perfect square that divides $12$ .
That's 4, since $4 \cdot 3 = 12$ .

STEP 5

So, we can rewrite $\sqrt{12}$ as $\sqrt{4 \cdot 3}$ .
Using the product property of square roots, this becomes $\sqrt{4} \cdot \sqrt{3}$ .

STEP 6

Since $\sqrt{4} = 2$ , our expression simplifies to $2\sqrt{3}$ .
We can't simplify $\sqrt{3}$ any further, because $3$ is a prime number.

STEP 7

Our final answer is $2\sqrt{3}$ .

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QuestionExpress 121212^{\frac{1}{2}}1221​ in simplest radical form.

Studdy Solution

STEP 1

What is this asking? We need to simplify 121212^{\frac{1}{2}}1221​ and write it using a radical. Watch out! Remember that fractional exponents can be rewritten as radicals, and don't forget to simplify the radical completely!

STEP 2

1. Rewrite the exponent as a radical.2. Simplify the radical.

STEP 3

Alright, let's **rewrite** this fractional exponent as a radical!Remember, a fractional exponent of 12\frac{1}{2}21​ means we're taking the **square root**.So, 121212^{\frac{1}{2}}1221​ is the same as 12\sqrt{12}12​.It's like translating from one mathematical language to another!

STEP 4

Now, let's **simplify** 12\sqrt{12}12​.We're looking for the largest **perfect square** that divides 121212.That's **4**, since 4⋅3=124 \cdot 3 = 124⋅3=12.

STEP 5

So, we can rewrite 12\sqrt{12}12​ as 4⋅3\sqrt{4 \cdot 3}4⋅3​.Using the **product property of square roots**, this becomes 4⋅3\sqrt{4} \cdot \sqrt{3}4​⋅3​.

STEP 6

Since 4=2\sqrt{4} = 24​=2, our expression simplifies to 232\sqrt{3}23​.We can't simplify 3\sqrt{3}3​ any further, because 333 is a **prime number**.

STEP 7

Our **final answer** is 232\sqrt{3}23​.

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QuestionExpress $12^{\frac{1}{2}}$ in simplest radical form.

What is this asking? We need to simplify $12^{\frac{1}{2}}$ and write it using a radical. Watch out! Remember that fractional exponents can be rewritten as radicals, and don't forget to simplify the radical completely!

1. Rewrite the exponent as a radical.
2. Simplify the radical.

Alright, let's rewrite this fractional exponent as a radical!
Remember, a fractional exponent of $\frac{1}{2}$ means we're taking the square root.
So, $12^{\frac{1}{2}}$ is the same as $\sqrt{12}$ .
It's like translating from one mathematical language to another!

Now, let's simplify $\sqrt{12}$ .
We're looking for the largest perfect square that divides $12$ .
That's 4, since $4 \cdot 3 = 12$ .

So, we can rewrite $\sqrt{12}$ as $\sqrt{4 \cdot 3}$ .
Using the product property of square roots, this becomes $\sqrt{4} \cdot \sqrt{3}$ .

Since $\sqrt{4} = 2$ , our expression simplifies to $2\sqrt{3}$ .
We can't simplify $\sqrt{3}$ any further, because $3$ is a prime number.

Our final answer is $2\sqrt{3}$ .