QuestionFind the equivalent expression for $\sqrt{200}$ from the options: A. $2 \sqrt{10}$ B. $10 \sqrt{2}$ C. $100 \sqrt{2}$ D. $2 \sqrt{100}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the expression $\sqrt{200}$ . . We can use the property of radicals that $\sqrt{ab} = \sqrt{a} \times \sqrt{b}$ .

STEP 2

First, we need to find the prime factorization of200. This will allow us to simplify the square root.

STEP 3

The prime factorization of200 is $2^3 \times5^2$ .

STEP 4

We can rewrite $\sqrt{200}$ as $\sqrt{2^3 \times^2}$ .

STEP 5

Using the property of radicals, we can rewrite this as $\sqrt{2^3} \times \sqrt{5^2}$ .

STEP 6

implify $\sqrt{2^3}$ and $\sqrt{5^2}$ .
$\sqrt{2^3} =2 \sqrt{2}$ $\sqrt{5^2} =5$

STEP 7

Multiply the results together to get the simplified form of $\sqrt{200}$ .
$\sqrt{200} =2 \sqrt{2} \times5$

STEP 8

implify the expression.
$\sqrt{200} =10 \sqrt{2}$ Therefore, the expression $\sqrt{200}$ is equivalent to $10 \sqrt{2}$ , which corresponds to option B.

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QuestionFind the equivalent expression for $\sqrt{200}$ from the options: A. $2 \sqrt{10}$ B. $10 \sqrt{2}$ C. $100 \sqrt{2}$ D. $2 \sqrt{100}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the expression $\sqrt{200}$ . . We can use the property of radicals that $\sqrt{ab} = \sqrt{a} \times \sqrt{b}$ .

STEP 2

First, we need to find the prime factorization of200. This will allow us to simplify the square root.

STEP 3

The prime factorization of200 is $2^3 \times5^2$ .

STEP 4

We can rewrite $\sqrt{200}$ as $\sqrt{2^3 \times^2}$ .

STEP 5

Using the property of radicals, we can rewrite this as $\sqrt{2^3} \times \sqrt{5^2}$ .

STEP 6

implify $\sqrt{2^3}$ and $\sqrt{5^2}$ .
$\sqrt{2^3} =2 \sqrt{2}$ $\sqrt{5^2} =5$

STEP 7

Multiply the results together to get the simplified form of $\sqrt{200}$ .
$\sqrt{200} =2 \sqrt{2} \times5$

STEP 8

implify the expression.
$\sqrt{200} =10 \sqrt{2}$ Therefore, the expression $\sqrt{200}$ is equivalent to $10 \sqrt{2}$ , which corresponds to option B.

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QuestionFind the equivalent expression for 200\sqrt{200}200​ from the options: A. 2102 \sqrt{10}210​ B. 10210 \sqrt{2}102​ C. 1002100 \sqrt{2}1002​ D. 21002 \sqrt{100}2100​.

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the expression 200\sqrt{200}200​. . We can use the property of radicals that ab=a×b\sqrt{ab} = \sqrt{a} \times \sqrt{b}ab​=a​×b​.

STEP 2

First, we need to find the prime factorization of200. This will allow us to simplify the square root.

STEP 3

The prime factorization of200 is 23×522^3 \times5^223×52.

STEP 4

We can rewrite 200\sqrt{200}200​ as 23×2\sqrt{2^3 \times^2}23×2​.

STEP 5

Using the property of radicals, we can rewrite this as 23×52\sqrt{2^3} \times \sqrt{5^2}23​×52​.

STEP 6

implify 23\sqrt{2^3}23​ and 52\sqrt{5^2}52​.23=22\sqrt{2^3} =2 \sqrt{2}23​=22​52=5\sqrt{5^2} =552​=5

STEP 7

Multiply the results together to get the simplified form of 200\sqrt{200}200​.200=22×5\sqrt{200} =2 \sqrt{2} \times5200​=22​×5

STEP 8

implify the expression.200=102\sqrt{200} =10 \sqrt{2}200​=102​Therefore, the expression 200\sqrt{200}200​ is equivalent to 10210 \sqrt{2}102​, which corresponds to option B.

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QuestionFind the equivalent expression for $\sqrt{200}$ from the options: A. $2 \sqrt{10}$ B. $10 \sqrt{2}$ C. $100 \sqrt{2}$ D. $2 \sqrt{100}$ .

Assumptions1. We are asked to simplify the expression $\sqrt{200}$ . . We can use the property of radicals that $\sqrt{ab} = \sqrt{a} \times \sqrt{b}$ .

The prime factorization of200 is $2^3 \times5^2$ .

We can rewrite $\sqrt{200}$ as $\sqrt{2^3 \times^2}$ .

Using the property of radicals, we can rewrite this as $\sqrt{2^3} \times \sqrt{5^2}$ .

implify $\sqrt{2^3}$ and $\sqrt{5^2}$ .
$\sqrt{2^3} =2 \sqrt{2}$ $\sqrt{5^2} =5$

Multiply the results together to get the simplified form of $\sqrt{200}$ .
$\sqrt{200} =2 \sqrt{2} \times5$

implify the expression.
$\sqrt{200} =10 \sqrt{2}$ Therefore, the expression $\sqrt{200}$ is equivalent to $10 \sqrt{2}$ , which corresponds to option B.