Math

QuestionFind y3\sqrt[3]{y} given that (3,8)=(3,y)(3,8)=(3, \sqrt{y}).

Studdy Solution

STEP 1

Assumptions1. The given equation is (3,8)=(3,y)(3,8)=(3, \sqrt{y}) . We need to find the value of y3\sqrt[3]{y}

STEP 2

From the given equation, we can equate the second elements of both ordered pairs since the first elements are equal.
8=y8 = \sqrt{y}

STEP 3

To find the value of yy, we can square both sides of the equation.
y=82y =8^2

STEP 4

Calculate the value of yy.
y=82=64y =8^2 =64

STEP 5

Now that we have the value of yy, we can find the value of y3\sqrt[3]{y} by substituting yy into the expression.
y3=643\sqrt[3]{y} = \sqrt[3]{64}

STEP 6

Calculate the value of y3\sqrt[3]{y}.
y3=643=4\sqrt[3]{y} = \sqrt[3]{64} =4So, y3=4\sqrt[3]{y} =4.

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