QuestionSimplify $\sqrt{80}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the square root of80. . The square root of a number is a value that, when multiplied by itself, gives the original number.
3. We can simplify the square root of a number by finding its prime factors and pairing them.

STEP 2

Let's find the prime factors of80. We start by dividing80 by the smallest prime number, which is2.
$80 =2 \times40$

STEP 3

We continue factoring the quotient until we can't factor it anymore. $40 =2 \times20$

STEP 4

We continue factoring the quotient until we can't factor it anymore. $20 =2 \times10$

STEP 5

We continue factoring the quotient until we can't factor it anymore. $10 =2 \times5$

STEP 6

Now, we have found all the prime factors of80. They are2,2,2,2, and5.
$80 =2 \times2 \times2 \times2 \times5$

STEP 7

We can simplify the square root of a number by pairing the prime factors. Each pair of the same number can come out of the square root. $\sqrt{80} = \sqrt{2 \times2 \times2 \times2 \times5}$

STEP 8

We can pair the2's together.
$\sqrt{80} = \sqrt{(2 \times2) \times (2 \times2) \times5}$

STEP 9

Each pair of the same number can come out of the square root. $\sqrt{80} =2 \times2 \times \sqrt{5}$

STEP 10

Multiply the numbers outside the square root.
$\sqrt{80} =4 \times \sqrt{5}$ So, the simplified form of $\sqrt{80}$ is $4\sqrt{5}$ .

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