Solved on Jan 12, 2024

Find the value of $d$ given the equation $d^{2}=21$ . Express the solution in simplest radical form.

STEP 1

Assumptions
1. We are given the equation $d^2 = 21$ .
2. We need to solve for $d$ .
3. The solution may involve a radical expression.

STEP 2

To solve for $d$ , we need to take the square root of both sides of the equation. This is because the square root is the inverse operation of squaring a number.
$d = \pm\sqrt{d^2}$

STEP 3

Apply the square root to both sides of the equation $d^2 = 21$ .
$d = \pm\sqrt{21}$

STEP 4

Since $21$ is not a perfect square, we leave it under the radical sign. However, we can simplify the radical if $21$ has any square factors.

STEP 5

Factor $21$ to see if there are any square factors. The prime factorization of $21$ is $3 \times 7$ , which does not contain any square factors.

STEP 6

Since there are no square factors, the simplest radical form of $\sqrt{21}$ is just $\sqrt{21}$ itself.

STEP 7

Therefore, the solution for $d$ is:
$d = \pm\sqrt{21}$
This means $d$ can be either $+\sqrt{21}$ or $-\sqrt{21}$ .

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Find the value of $d$ given the equation $d^{2}=21$ . Express the solution in simplest radical form.

STEP 1

Assumptions
1. We are given the equation $d^2 = 21$ .
2. We need to solve for $d$ .
3. The solution may involve a radical expression.

STEP 2

To solve for $d$ , we need to take the square root of both sides of the equation. This is because the square root is the inverse operation of squaring a number.
$d = \pm\sqrt{d^2}$

STEP 3

Apply the square root to both sides of the equation $d^2 = 21$ .
$d = \pm\sqrt{21}$

STEP 4

Since $21$ is not a perfect square, we leave it under the radical sign. However, we can simplify the radical if $21$ has any square factors.

STEP 5

Factor $21$ to see if there are any square factors. The prime factorization of $21$ is $3 \times 7$ , which does not contain any square factors.

STEP 6

Since there are no square factors, the simplest radical form of $\sqrt{21}$ is just $\sqrt{21}$ itself.

STEP 7

Therefore, the solution for $d$ is:
$d = \pm\sqrt{21}$
This means $d$ can be either $+\sqrt{21}$ or $-\sqrt{21}$ .

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Find the value of ddd given the equation d2=21d^{2}=21d2=21. Express the solution in simplest radical form.

STEP 1

Assumptions1. We are given the equation d2=21d^2 = 21d2=21.2. We need to solve for ddd.3. The solution may involve a radical expression.

STEP 2

To solve for ddd, we need to take the square root of both sides of the equation. This is because the square root is the inverse operation of squaring a number.d=±d2d = \pm\sqrt{d^2}d=±d2​

STEP 3

Apply the square root to both sides of the equation d2=21d^2 = 21d2=21.d=±21d = \pm\sqrt{21}d=±21​

STEP 4

Since 212121 is not a perfect square, we leave it under the radical sign. However, we can simplify the radical if 212121 has any square factors.

STEP 5

Factor 212121 to see if there are any square factors. The prime factorization of 212121 is 3×73 \times 73×7, which does not contain any square factors.

STEP 6

Since there are no square factors, the simplest radical form of 21\sqrt{21}21​ is just 21\sqrt{21}21​ itself.

STEP 7

Therefore, the solution for ddd is:d=±21d = \pm\sqrt{21}d=±21​This means ddd can be either +21+\sqrt{21}+21​ or −21-\sqrt{21}−21​.

Start learning now

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

Find the value of $d$ given the equation $d^{2}=21$ . Express the solution in simplest radical form.

Assumptions
1. We are given the equation $d^2 = 21$ .
2. We need to solve for $d$ .
3. The solution may involve a radical expression.

To solve for $d$ , we need to take the square root of both sides of the equation. This is because the square root is the inverse operation of squaring a number.
$d = \pm\sqrt{d^2}$

Apply the square root to both sides of the equation $d^2 = 21$ .
$d = \pm\sqrt{21}$

Since $21$ is not a perfect square, we leave it under the radical sign. However, we can simplify the radical if $21$ has any square factors.

Factor $21$ to see if there are any square factors. The prime factorization of $21$ is $3 \times 7$ , which does not contain any square factors.

Since there are no square factors, the simplest radical form of $\sqrt{21}$ is just $\sqrt{21}$ itself.

Therefore, the solution for $d$ is:
$d = \pm\sqrt{21}$
This means $d$ can be either $+\sqrt{21}$ or $-\sqrt{21}$ .