Math / Numbers & Operations

QuestionSimplify. $\sqrt{550}$ $25 \sqrt{5}$ $5 \sqrt{11}$ $10 \sqrt{55}$ $5 \sqrt{22}$

Studdy Solution

STEP 1

1. We need to simplify the expression $\sqrt{550}$ .
2. We will compare the simplified form to the given options: $25 \sqrt{5}$ , $5 \sqrt{11}$ , $10 \sqrt{55}$ , $5 \sqrt{22}$ .

STEP 2

1. Factor the number under the square root.
2. Simplify the square root.
3. Compare the simplified form to the given options.

STEP 3

Factor $550$ into its prime factors.
$550 = 2 \times 5^2 \times 11$

STEP 4

Simplify $\sqrt{550}$ using the prime factors.
$\sqrt{550} = \sqrt{2 \times 5^2 \times 11}$

STEP 5

Extract the square of $5$ from the square root.
$\sqrt{550} = \sqrt{2 \times 5^2 \times 11} = 5 \sqrt{2 \times 11} = 5 \sqrt{22}$

STEP 6

Compare the simplified form $5 \sqrt{22}$ to the given options.
The simplified form matches the option $5 \sqrt{22}$ .
The simplified form of $\sqrt{550}$ is:
$\boxed{5 \sqrt{22}}$

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QuestionSimplify. $\sqrt{550}$ $25 \sqrt{5}$ $5 \sqrt{11}$ $10 \sqrt{55}$ $5 \sqrt{22}$

Studdy Solution

STEP 1

1. We need to simplify the expression $\sqrt{550}$ .
2. We will compare the simplified form to the given options: $25 \sqrt{5}$ , $5 \sqrt{11}$ , $10 \sqrt{55}$ , $5 \sqrt{22}$ .

STEP 2

1. Factor the number under the square root.
2. Simplify the square root.
3. Compare the simplified form to the given options.

STEP 3

Factor $550$ into its prime factors.
$550 = 2 \times 5^2 \times 11$

STEP 4

Simplify $\sqrt{550}$ using the prime factors.
$\sqrt{550} = \sqrt{2 \times 5^2 \times 11}$

STEP 5

Extract the square of $5$ from the square root.
$\sqrt{550} = \sqrt{2 \times 5^2 \times 11} = 5 \sqrt{2 \times 11} = 5 \sqrt{22}$

STEP 6

Compare the simplified form $5 \sqrt{22}$ to the given options.
The simplified form matches the option $5 \sqrt{22}$ .
The simplified form of $\sqrt{550}$ is:
$\boxed{5 \sqrt{22}}$

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QuestionSimplify. 550\sqrt{550}550​ 25525 \sqrt{5}255​ 5115 \sqrt{11}511​ 105510 \sqrt{55}1055​ 5225 \sqrt{22}522​

Studdy Solution

STEP 1

1. We need to simplify the expression 550\sqrt{550}550​.2. We will compare the simplified form to the given options: 25525 \sqrt{5}255​, 5115 \sqrt{11}511​, 105510 \sqrt{55}1055​, 5225 \sqrt{22}522​.

STEP 2

1. Factor the number under the square root.2. Simplify the square root.3. Compare the simplified form to the given options.

STEP 3

Factor 550550550 into its prime factors.550=2×52×11 550 = 2 \times 5^2 \times 11 550=2×52×11

STEP 4

Simplify 550\sqrt{550}550​ using the prime factors.550=2×52×11\sqrt{550} = \sqrt{2 \times 5^2 \times 11}550​=2×52×11​

STEP 5

Extract the square of 555 from the square root.550=2×52×11=52×11=522\sqrt{550} = \sqrt{2 \times 5^2 \times 11} = 5 \sqrt{2 \times 11} = 5 \sqrt{22}550​=2×52×11​=52×11​=522​

STEP 6

Compare the simplified form 5225 \sqrt{22}522​ to the given options.The simplified form matches the option 5225 \sqrt{22}522​. The simplified form of 550\sqrt{550}550​ is:522\boxed{5 \sqrt{22}}522​​

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QuestionSimplify. $\sqrt{550}$ $25 \sqrt{5}$ $5 \sqrt{11}$ $10 \sqrt{55}$ $5 \sqrt{22}$

1. We need to simplify the expression $\sqrt{550}$ .
2. We will compare the simplified form to the given options: $25 \sqrt{5}$ , $5 \sqrt{11}$ , $10 \sqrt{55}$ , $5 \sqrt{22}$ .

1. Factor the number under the square root.
2. Simplify the square root.
3. Compare the simplified form to the given options.

Factor $550$ into its prime factors.
$550 = 2 \times 5^2 \times 11$

Simplify $\sqrt{550}$ using the prime factors.
$\sqrt{550} = \sqrt{2 \times 5^2 \times 11}$

Extract the square of $5$ from the square root.
$\sqrt{550} = \sqrt{2 \times 5^2 \times 11} = 5 \sqrt{2 \times 11} = 5 \sqrt{22}$

Compare the simplified form $5 \sqrt{22}$ to the given options.
The simplified form matches the option $5 \sqrt{22}$ .
The simplified form of $\sqrt{550}$ is:
$\boxed{5 \sqrt{22}}$