Question Simplify the square root expression $-\frac{1}{7} \sqrt{98}$ .

Studdy Solution

STEP 1

Assumptions
1. We need to simplify the expression $-\frac{1}{7} \sqrt{98}$ .
2. To take a factor out of the square root, we look for a perfect square factor of the number inside the square root.

STEP 2

Identify the perfect square factors of 98.
98 can be factored into $2 \times 49$ , and 49 is a perfect square ( $7^2$ ).

STEP 3

Rewrite the square root of 98 by separating the perfect square factor.
$\sqrt{98} = \sqrt{2 \times 49}$

STEP 4

Use the property of square roots that $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ to separate the square root of the product into the product of square roots.
$\sqrt{98} = \sqrt{2} \times \sqrt{49}$

STEP 5

Calculate the square root of the perfect square factor.
$\sqrt{49} = 7$

STEP 6

Substitute the square root of the perfect square factor back into the expression.
$\sqrt{98} = \sqrt{2} \times 7$

STEP 7

Now, we can simplify the original expression by including the factor we took out of the square root.
$-\frac{1}{7} \sqrt{98} = -\frac{1}{7} \times (\sqrt{2} \times 7)$

STEP 8

Notice that the $7$ outside the square root and the $-\frac{1}{7}$ can be simplified.
$-\frac{1}{7} \times (\sqrt{2} \times 7) = -\sqrt{2}$

STEP 9

The expression is now simplified.
The simplified form of $-\frac{1}{7} \sqrt{98}$ is $-\sqrt{2}$ .

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Question Simplify the square root expression $-\frac{1}{7} \sqrt{98}$ .

Studdy Solution

STEP 1

Assumptions
1. We need to simplify the expression $-\frac{1}{7} \sqrt{98}$ .
2. To take a factor out of the square root, we look for a perfect square factor of the number inside the square root.

STEP 2

Identify the perfect square factors of 98.
98 can be factored into $2 \times 49$ , and 49 is a perfect square ( $7^2$ ).

STEP 3

Rewrite the square root of 98 by separating the perfect square factor.
$\sqrt{98} = \sqrt{2 \times 49}$

STEP 4

Use the property of square roots that $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ to separate the square root of the product into the product of square roots.
$\sqrt{98} = \sqrt{2} \times \sqrt{49}$

STEP 5

Calculate the square root of the perfect square factor.
$\sqrt{49} = 7$

STEP 6

Substitute the square root of the perfect square factor back into the expression.
$\sqrt{98} = \sqrt{2} \times 7$

STEP 7

Now, we can simplify the original expression by including the factor we took out of the square root.
$-\frac{1}{7} \sqrt{98} = -\frac{1}{7} \times (\sqrt{2} \times 7)$

STEP 8

Notice that the $7$ outside the square root and the $-\frac{1}{7}$ can be simplified.
$-\frac{1}{7} \times (\sqrt{2} \times 7) = -\sqrt{2}$

STEP 9

The expression is now simplified.
The simplified form of $-\frac{1}{7} \sqrt{98}$ is $-\sqrt{2}$ .

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Question Simplify the square root expression −1798-\frac{1}{7} \sqrt{98}−71​98​.

Studdy Solution

STEP 1

Assumptions1. We need to simplify the expression −1798-\frac{1}{7} \sqrt{98}−71​98​.2. To take a factor out of the square root, we look for a perfect square factor of the number inside the square root.

STEP 2

Identify the perfect square factors of 98.98 can be factored into 2×492 \times 492×49, and 49 is a perfect square (727^272).

STEP 3

Rewrite the square root of 98 by separating the perfect square factor.98=2×49\sqrt{98} = \sqrt{2 \times 49}98​=2×49​

STEP 4

Use the property of square roots that a×b=a×b\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}a×b​=a​×b​ to separate the square root of the product into the product of square roots.98=2×49\sqrt{98} = \sqrt{2} \times \sqrt{49}98​=2​×49​

STEP 5

Calculate the square root of the perfect square factor.49=7\sqrt{49} = 749​=7

STEP 6

Substitute the square root of the perfect square factor back into the expression.98=2×7\sqrt{98} = \sqrt{2} \times 798​=2​×7

STEP 7

Now, we can simplify the original expression by including the factor we took out of the square root.−1798=−17×(2×7)-\frac{1}{7} \sqrt{98} = -\frac{1}{7} \times (\sqrt{2} \times 7)−71​98​=−71​×(2​×7)

STEP 8

Notice that the 777 outside the square root and the −17-\frac{1}{7}−71​ can be simplified.−17×(2×7)=−2-\frac{1}{7} \times (\sqrt{2} \times 7) = -\sqrt{2}−71​×(2​×7)=−2​

STEP 9

The expression is now simplified.The simplified form of −1798-\frac{1}{7} \sqrt{98}−71​98​ is −2-\sqrt{2}−2​.

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Question Simplify the square root expression $-\frac{1}{7} \sqrt{98}$ .

Assumptions
1. We need to simplify the expression $-\frac{1}{7} \sqrt{98}$ .
2. To take a factor out of the square root, we look for a perfect square factor of the number inside the square root.

Identify the perfect square factors of 98.
98 can be factored into $2 \times 49$ , and 49 is a perfect square ( $7^2$ ).

Rewrite the square root of 98 by separating the perfect square factor.
$\sqrt{98} = \sqrt{2 \times 49}$

Use the property of square roots that $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ to separate the square root of the product into the product of square roots.
$\sqrt{98} = \sqrt{2} \times \sqrt{49}$

Calculate the square root of the perfect square factor.
$\sqrt{49} = 7$

Substitute the square root of the perfect square factor back into the expression.
$\sqrt{98} = \sqrt{2} \times 7$

Now, we can simplify the original expression by including the factor we took out of the square root.
$-\frac{1}{7} \sqrt{98} = -\frac{1}{7} \times (\sqrt{2} \times 7)$

Notice that the $7$ outside the square root and the $-\frac{1}{7}$ can be simplified.
$-\frac{1}{7} \times (\sqrt{2} \times 7) = -\sqrt{2}$

The expression is now simplified.
The simplified form of $-\frac{1}{7} \sqrt{98}$ is $-\sqrt{2}$ .