QuestionSimplify $\sqrt{63}$ and express it in the form $\sqrt{(\square)}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the square root of63. . We can simplify a square root by factoring the number under the root into its prime factors.
3. We can then pair the prime factors and take one factor from each pair out from under the root.

STEP 2

First, we need to factorize63 into its prime factors. The prime factors of63 are and7.
$63 = \times \times7$

STEP 3

Now, we rewrite the square root of63 using its prime factors.
$\sqrt{63} = \sqrt{3 \times3 \times7}$

STEP 4

We can rewrite the square root as a product of square roots.
$\sqrt{3 \times3 \times7} = \sqrt{3^2} \times \sqrt{7}$

STEP 5

The square root of a square number is the number itself. So, we can simplify $\sqrt{3^2}$ to3.
$\sqrt{3^2} \times \sqrt{7} =3 \times \sqrt{7}$ So, the simplified form of $\sqrt{63}$ is $3\sqrt{7}$ .

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QuestionSimplify $\sqrt{63}$ and express it in the form $\sqrt{(\square)}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the square root of63. . We can simplify a square root by factoring the number under the root into its prime factors.
3. We can then pair the prime factors and take one factor from each pair out from under the root.

STEP 2

First, we need to factorize63 into its prime factors. The prime factors of63 are and7.
$63 = \times \times7$

STEP 3

Now, we rewrite the square root of63 using its prime factors.
$\sqrt{63} = \sqrt{3 \times3 \times7}$

STEP 4

We can rewrite the square root as a product of square roots.
$\sqrt{3 \times3 \times7} = \sqrt{3^2} \times \sqrt{7}$

STEP 5

The square root of a square number is the number itself. So, we can simplify $\sqrt{3^2}$ to3.
$\sqrt{3^2} \times \sqrt{7} =3 \times \sqrt{7}$ So, the simplified form of $\sqrt{63}$ is $3\sqrt{7}$ .

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QuestionSimplify 63\sqrt{63}63​ and express it in the form (□)\sqrt{(\square)}(□)​.

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the square root of63. . We can simplify a square root by factoring the number under the root into its prime factors.3. We can then pair the prime factors and take one factor from each pair out from under the root.

STEP 2

First, we need to factorize63 into its prime factors. The prime factors of63 are and7.63=××763 = \times \times763=××7

STEP 3

Now, we rewrite the square root of63 using its prime factors.63=3×3×7\sqrt{63} = \sqrt{3 \times3 \times7}63​=3×3×7​

STEP 4

We can rewrite the square root as a product of square roots.3×3×7=32×7\sqrt{3 \times3 \times7} = \sqrt{3^2} \times \sqrt{7}3×3×7​=32​×7​

STEP 5

The square root of a square number is the number itself. So, we can simplify 32\sqrt{3^2}32​ to3.32×7=3×7\sqrt{3^2} \times \sqrt{7} =3 \times \sqrt{7}32​×7​=3×7​So, the simplified form of 63\sqrt{63}63​ is 373\sqrt{7}37​.

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QuestionSimplify $\sqrt{63}$ and express it in the form $\sqrt{(\square)}$ .

Assumptions1. We are asked to simplify the square root of63. . We can simplify a square root by factoring the number under the root into its prime factors.
3. We can then pair the prime factors and take one factor from each pair out from under the root.

First, we need to factorize63 into its prime factors. The prime factors of63 are and7.
$63 = \times \times7$

Now, we rewrite the square root of63 using its prime factors.
$\sqrt{63} = \sqrt{3 \times3 \times7}$

We can rewrite the square root as a product of square roots.
$\sqrt{3 \times3 \times7} = \sqrt{3^2} \times \sqrt{7}$

The square root of a square number is the number itself. So, we can simplify $\sqrt{3^2}$ to3.
$\sqrt{3^2} \times \sqrt{7} =3 \times \sqrt{7}$ So, the simplified form of $\sqrt{63}$ is $3\sqrt{7}$ .