Math

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

Studdy Solution

STEP 1

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

STEP 2

To solve for dd, 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}

STEP 3

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

STEP 4

Since 2121 is not a perfect square, we leave it under the radical sign. However, we can simplify the radical if 2121 has any square factors.

STEP 5

Factor 2121 to see if there are any square factors. The prime factorization of 2121 is 3×73 \times 7, which does not contain any square factors.

STEP 6

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

STEP 7

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

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