Math

QuestionSimplify 52\sqrt{-52} and find the result among these options: i13i \sqrt{13}, 2i132 i \sqrt{13}, 213-2 \sqrt{13}, 2132-\sqrt{13}.

Studdy Solution

STEP 1

Assumptions1. The problem is to simplify 52\sqrt{-52}

STEP 2

We know that the square root of a negative number is an imaginary number. We can express the square root of a negative number as ii times the square root of the absolute value of the number.
a=ia\sqrt{-a} = i \sqrt{a}

STEP 3

Now, plug in the given value for aa to calculate the square root of -52.
52=i52\sqrt{-52} = i \sqrt{52}

STEP 4

We can simplify 52\sqrt{52} by factoring52 into4 and13.
52=4×13\sqrt{52} = \sqrt{4 \times13}

STEP 5

We can simplify further by taking the square root of4.
52=213\sqrt{52} =2 \sqrt{13}

STEP 6

Now, substitute 52\sqrt{52} with 2132 \sqrt{13} in the equation from3.
52=i×213\sqrt{-52} = i \times2 \sqrt{13}

STEP 7

Finally, we simplify the expression to get the final answer.
52=2i13\sqrt{-52} =2i \sqrt{13}So, the simplified form of 52\sqrt{-52} is 2i132i \sqrt{13}.

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