Solved on Jan 13, 2024

Find the square root of 784 using prime factorization.

STEP 1

Assumptions
1. We need to find the square root of 784.
2. We will use prime factorization to find the square root.

STEP 2

Begin the prime factorization of 784 by finding the smallest prime number that divides 784.
$784 \div 2 = 392$

STEP 3

Continue the prime factorization with the quotient.
$392 \div 2 = 196$

STEP 4

Continue the prime factorization.
$196 \div 2 = 98$

STEP 5

Continue the prime factorization.
$98 \div 2 = 49$

STEP 6

Since 49 is not divisible by 2, we find the next smallest prime number, which is 7.
$49 \div 7 = 7$

STEP 7

Continue the prime factorization.
$7 \div 7 = 1$

STEP 8

Now that we have reached 1, we can stop the prime factorization. The prime factors of 784 are:
$784 = 2 \times 2 \times 2 \times 2 \times 7 \times 7$

STEP 9

To find the square root, we pair the prime factors into pairs of identical factors.
$\sqrt{784} = \sqrt{2 \times 2 \times 2 \times 2 \times 7 \times 7}$

STEP 10

Take one factor from each pair out of the square root.
$\sqrt{784} = 2 \times 2 \times 7$

STEP 11

Multiply the factors outside the square root to find the square root of 784.
$\sqrt{784} = 2 \times 2 \times 7 = 4 \times 7 = 28$
The square root of 784 is 28.

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Find the square root of 784 using prime factorization.

STEP 1

Assumptions
1. We need to find the square root of 784.
2. We will use prime factorization to find the square root.

STEP 2

Begin the prime factorization of 784 by finding the smallest prime number that divides 784.
$784 \div 2 = 392$

STEP 3

Continue the prime factorization with the quotient.
$392 \div 2 = 196$

STEP 4

Continue the prime factorization.
$196 \div 2 = 98$

STEP 5

Continue the prime factorization.
$98 \div 2 = 49$

STEP 6

Since 49 is not divisible by 2, we find the next smallest prime number, which is 7.
$49 \div 7 = 7$

STEP 7

Continue the prime factorization.
$7 \div 7 = 1$

STEP 8

Now that we have reached 1, we can stop the prime factorization. The prime factors of 784 are:
$784 = 2 \times 2 \times 2 \times 2 \times 7 \times 7$

STEP 9

To find the square root, we pair the prime factors into pairs of identical factors.
$\sqrt{784} = \sqrt{2 \times 2 \times 2 \times 2 \times 7 \times 7}$

STEP 10

Take one factor from each pair out of the square root.
$\sqrt{784} = 2 \times 2 \times 7$

STEP 11

Multiply the factors outside the square root to find the square root of 784.
$\sqrt{784} = 2 \times 2 \times 7 = 4 \times 7 = 28$
The square root of 784 is 28.

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Find the square root of 784 using prime factorization.

STEP 1

Assumptions1. We need to find the square root of 784.2. We will use prime factorization to find the square root.

STEP 2

Begin the prime factorization of 784 by finding the smallest prime number that divides 784.784÷2=392784 \div 2 = 392784÷2=392

STEP 3

Continue the prime factorization with the quotient.392÷2=196392 \div 2 = 196392÷2=196

STEP 4

Continue the prime factorization.196÷2=98196 \div 2 = 98196÷2=98

STEP 5

Continue the prime factorization.98÷2=4998 \div 2 = 4998÷2=49

STEP 6

Since 49 is not divisible by 2, we find the next smallest prime number, which is 7.49÷7=749 \div 7 = 749÷7=7

STEP 7

Continue the prime factorization.7÷7=17 \div 7 = 17÷7=1

STEP 8

Now that we have reached 1, we can stop the prime factorization. The prime factors of 784 are:784=2×2×2×2×7×7784 = 2 \times 2 \times 2 \times 2 \times 7 \times 7784=2×2×2×2×7×7

STEP 9

To find the square root, we pair the prime factors into pairs of identical factors.784=2×2×2×2×7×7\sqrt{784} = \sqrt{2 \times 2 \times 2 \times 2 \times 7 \times 7}784​=2×2×2×2×7×7​

STEP 10

Take one factor from each pair out of the square root.784=2×2×7\sqrt{784} = 2 \times 2 \times 7784​=2×2×7

STEP 11

Multiply the factors outside the square root to find the square root of 784.784=2×2×7=4×7=28\sqrt{784} = 2 \times 2 \times 7 = 4 \times 7 = 28784​=2×2×7=4×7=28The square root of 784 is 28.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions
1. We need to find the square root of 784.
2. We will use prime factorization to find the square root.

Begin the prime factorization of 784 by finding the smallest prime number that divides 784.
$784 \div 2 = 392$

Continue the prime factorization with the quotient.
$392 \div 2 = 196$

Continue the prime factorization.
$196 \div 2 = 98$

Continue the prime factorization.
$98 \div 2 = 49$

Since 49 is not divisible by 2, we find the next smallest prime number, which is 7.
$49 \div 7 = 7$

Continue the prime factorization.
$7 \div 7 = 1$

Now that we have reached 1, we can stop the prime factorization. The prime factors of 784 are:
$784 = 2 \times 2 \times 2 \times 2 \times 7 \times 7$

To find the square root, we pair the prime factors into pairs of identical factors.
$\sqrt{784} = \sqrt{2 \times 2 \times 2 \times 2 \times 7 \times 7}$

Take one factor from each pair out of the square root.
$\sqrt{784} = 2 \times 2 \times 7$

Multiply the factors outside the square root to find the square root of 784.
$\sqrt{784} = 2 \times 2 \times 7 = 4 \times 7 = 28$
The square root of 784 is 28.