QuestionSimplify $\sqrt{147}$ . Options: A. $21 \sqrt{7}$ B. $49 \sqrt{3}$ C. $7 \sqrt{3}$ D. $3 \sqrt{7}$

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the square root of147. The square root of a number is a value that, when multiplied by itself, gives the original number3. We can simplify the square root of a number by finding its prime factors and pairing them

STEP 2

First, we need to find the prime factors of147. Prime factors are the prime numbers that divide a number exactly.

STEP 3

We start by dividing147 by the smallest prime number, which is2. But147 is not divisible by2, so we try the next prime number, which is3. $147 /3 =49$ So,3 is a prime factor of147.

STEP 4

Next, we divide49 by the smallest prime number, which is2. But49 is not divisible by2, so we try the next prime number, which is3. But49 is not divisible by3 either, so we try the next prime number, which is. But49 is not divisible by either, so we try the next prime number, which is7.
$49 /7 =7$ So,7 is a prime factor of49.

STEP 5

Finally, we divide7 by the smallest prime number, which is2. But7 is not divisible by2, so we try the next prime number, which is3. But7 is not divisible by3 either, so we try the next prime number, which is5. But7 is not divisible by5 either, so we try the next prime number, which is7.
$7 /7 =1$ So,7 is a prime factor of7.

STEP 6

Now that we have found all the prime factors of147, we can write147 as the product of its prime factors.
$147 =3 \\times \\times$

STEP 7

We can simplify the square root of147 by pairing the prime factors. Each pair of identical factors can come out of the square root.
$\sqrt{147} = \sqrt{3 \\times7 \\times7}$

STEP 8

Take out the pair of7 from under the square root.
$\sqrt{147} =7 \sqrt{3}$ Therefore, the simplified form of $\sqrt{147}$ is $7 \sqrt{3}$ , so the correct answer is C. $7 \sqrt{3}$ .

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QuestionSimplify $\sqrt{147}$ . Options: A. $21 \sqrt{7}$ B. $49 \sqrt{3}$ C. $7 \sqrt{3}$ D. $3 \sqrt{7}$

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the square root of147. The square root of a number is a value that, when multiplied by itself, gives the original number3. We can simplify the square root of a number by finding its prime factors and pairing them

STEP 2

First, we need to find the prime factors of147. Prime factors are the prime numbers that divide a number exactly.

STEP 3

We start by dividing147 by the smallest prime number, which is2. But147 is not divisible by2, so we try the next prime number, which is3. $147 /3 =49$ So,3 is a prime factor of147.

STEP 4

STEP 5

STEP 6

Now that we have found all the prime factors of147, we can write147 as the product of its prime factors.
$147 =3 \\times \\times$

STEP 7

We can simplify the square root of147 by pairing the prime factors. Each pair of identical factors can come out of the square root.
$\sqrt{147} = \sqrt{3 \\times7 \\times7}$

STEP 8

Take out the pair of7 from under the square root.
$\sqrt{147} =7 \sqrt{3}$ Therefore, the simplified form of $\sqrt{147}$ is $7 \sqrt{3}$ , so the correct answer is C. $7 \sqrt{3}$ .

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QuestionSimplify 147\sqrt{147}147​. Options: A. 21721 \sqrt{7}217​ B. 49349 \sqrt{3}493​ C. 737 \sqrt{3}73​ D. 373 \sqrt{7}37​

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the square root of147. The square root of a number is a value that, when multiplied by itself, gives the original number3. We can simplify the square root of a number by finding its prime factors and pairing them

STEP 2

First, we need to find the prime factors of147. Prime factors are the prime numbers that divide a number exactly.

STEP 3

We start by dividing147 by the smallest prime number, which is2. But147 is not divisible by2, so we try the next prime number, which is3.147/3=49147 /3 =49147/3=49So,3 is a prime factor of147.

STEP 4

STEP 5

STEP 6

Now that we have found all the prime factors of147, we can write147 as the product of its prime factors.147=3timestimes147 =3 \\times \\times147=3timestimes

STEP 7

We can simplify the square root of147 by pairing the prime factors. Each pair of identical factors can come out of the square root.147=3times7times7\sqrt{147} = \sqrt{3 \\times7 \\times7}147​=3times7times7​

STEP 8

Take out the pair of7 from under the square root.147=73\sqrt{147} =7 \sqrt{3}147​=73​Therefore, the simplified form of 147\sqrt{147}147​ is 737 \sqrt{3}73​, so the correct answer is C. 737 \sqrt{3}73​.

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QuestionSimplify $\sqrt{147}$ . Options: A. $21 \sqrt{7}$ B. $49 \sqrt{3}$ C. $7 \sqrt{3}$ D. $3 \sqrt{7}$

We start by dividing147 by the smallest prime number, which is2. But147 is not divisible by2, so we try the next prime number, which is3. $147 /3 =49$ So,3 is a prime factor of147.

Now that we have found all the prime factors of147, we can write147 as the product of its prime factors.
$147 =3 \\times \\times$

We can simplify the square root of147 by pairing the prime factors. Each pair of identical factors can come out of the square root.
$\sqrt{147} = \sqrt{3 \\times7 \\times7}$

Take out the pair of7 from under the square root.
$\sqrt{147} =7 \sqrt{3}$ Therefore, the simplified form of $\sqrt{147}$ is $7 \sqrt{3}$ , so the correct answer is C. $7 \sqrt{3}$ .