QuestionSimplify $\sqrt{3} \cdot \sqrt{21}$ and provide the answer in exact form.

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the expression $\sqrt{3} \cdot \sqrt{21}$ . . We are allowed to use the property of square roots that states $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$ .

STEP 2

First, we will use the property of square roots to combine the two square roots into one. $\sqrt{} \cdot \sqrt{21} = \sqrt{ \cdot21}$

STEP 3

Next, we will calculate the product inside the square root.
$\sqrt{3 \cdot21} = \sqrt{63}$

STEP 4

Now, we will simplify the square root by factoring the number inside the square root into its prime factors.
$\sqrt{63} = \sqrt{3^2 \cdot7}$

STEP 5

We can now simplify the square root using the rule $\sqrt{a^2} = a$ .
$\sqrt{3^2 \cdot7} =3\sqrt{7}$ So, $\sqrt{3} \cdot \sqrt{21}$ simplifies to $3\sqrt{7}$ .

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QuestionSimplify $\sqrt{3} \cdot \sqrt{21}$ and provide the answer in exact form.

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the expression $\sqrt{3} \cdot \sqrt{21}$ . . We are allowed to use the property of square roots that states $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$ .

STEP 2

First, we will use the property of square roots to combine the two square roots into one. $\sqrt{} \cdot \sqrt{21} = \sqrt{ \cdot21}$

STEP 3

Next, we will calculate the product inside the square root.
$\sqrt{3 \cdot21} = \sqrt{63}$

STEP 4

Now, we will simplify the square root by factoring the number inside the square root into its prime factors.
$\sqrt{63} = \sqrt{3^2 \cdot7}$

STEP 5

We can now simplify the square root using the rule $\sqrt{a^2} = a$ .
$\sqrt{3^2 \cdot7} =3\sqrt{7}$ So, $\sqrt{3} \cdot \sqrt{21}$ simplifies to $3\sqrt{7}$ .

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QuestionSimplify 3⋅21\sqrt{3} \cdot \sqrt{21}3​⋅21​ and provide the answer in exact form.

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the expression 3⋅21\sqrt{3} \cdot \sqrt{21}3​⋅21​. . We are allowed to use the property of square roots that states a⋅b=ab\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}a​⋅b​=ab​.

STEP 2

First, we will use the property of square roots to combine the two square roots into one.⋅21=⋅21\sqrt{} \cdot \sqrt{21} = \sqrt{ \cdot21}​⋅21​=⋅21​

STEP 3

Next, we will calculate the product inside the square root.3⋅21=63\sqrt{3 \cdot21} = \sqrt{63}3⋅21​=63​

STEP 4

Now, we will simplify the square root by factoring the number inside the square root into its prime factors.63=32⋅7\sqrt{63} = \sqrt{3^2 \cdot7}63​=32⋅7​

STEP 5

We can now simplify the square root using the rule a2=a\sqrt{a^2} = aa2​=a.32⋅7=37\sqrt{3^2 \cdot7} =3\sqrt{7}32⋅7​=37​So, 3⋅21\sqrt{3} \cdot \sqrt{21}3​⋅21​ simplifies to 373\sqrt{7}37​.

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QuestionSimplify $\sqrt{3} \cdot \sqrt{21}$ and provide the answer in exact form.

Assumptions1. We are asked to simplify the expression $\sqrt{3} \cdot \sqrt{21}$ . . We are allowed to use the property of square roots that states $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$ .

First, we will use the property of square roots to combine the two square roots into one. $\sqrt{} \cdot \sqrt{21} = \sqrt{ \cdot21}$

Next, we will calculate the product inside the square root.
$\sqrt{3 \cdot21} = \sqrt{63}$

Now, we will simplify the square root by factoring the number inside the square root into its prime factors.
$\sqrt{63} = \sqrt{3^2 \cdot7}$

We can now simplify the square root using the rule $\sqrt{a^2} = a$ .
$\sqrt{3^2 \cdot7} =3\sqrt{7}$ So, $\sqrt{3} \cdot \sqrt{21}$ simplifies to $3\sqrt{7}$ .