Solved on Jan 22, 2024

Simplify $\sqrt{121 z^{2}}$

STEP 1

Assumptions
1. We are given the radical expression $\sqrt{121 z^{2}}$ .
2. We need to simplify the expression by factoring out perfect squares from under the radical.

STEP 2

Identify the perfect square factors in the given expression.
The number 121 is a perfect square since $11^2 = 121$ , and $z^2$ is also a perfect square.

STEP 3

Rewrite the radical expression by separating the perfect square factors.
$\sqrt{121 z^{2}} = \sqrt{121} \cdot \sqrt{z^{2}}$

STEP 4

Take the square root of the perfect squares.
Since the square root of a perfect square is the number that was squared, we have:
$\sqrt{121} = 11$ $\sqrt{z^{2}} = z$

STEP 5

Multiply the results of the square roots.
$11 \cdot z = 11z$

STEP 6

Write the simplified expression.
The simplified form of $\sqrt{121 z^{2}}$ is $11z$ .
Karan needs to pay $803 each month.

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Simplify $\sqrt{121 z^{2}}$

STEP 1

Assumptions
1. We are given the radical expression $\sqrt{121 z^{2}}$ .
2. We need to simplify the expression by factoring out perfect squares from under the radical.

STEP 2

Identify the perfect square factors in the given expression.
The number 121 is a perfect square since $11^2 = 121$ , and $z^2$ is also a perfect square.

STEP 3

Rewrite the radical expression by separating the perfect square factors.
$\sqrt{121 z^{2}} = \sqrt{121} \cdot \sqrt{z^{2}}$

STEP 4

Take the square root of the perfect squares.
Since the square root of a perfect square is the number that was squared, we have:
$\sqrt{121} = 11$ $\sqrt{z^{2}} = z$

STEP 5

Multiply the results of the square roots.
$11 \cdot z = 11z$

STEP 6

Write the simplified expression.
The simplified form of $\sqrt{121 z^{2}}$ is $11z$ .
Karan needs to pay $803 each month.

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Simplify 121z2\sqrt{121 z^{2}}121z2​

STEP 1

Assumptions1. We are given the radical expression 121z2\sqrt{121 z^{2}}121z2​.2. We need to simplify the expression by factoring out perfect squares from under the radical.

STEP 2

Identify the perfect square factors in the given expression.The number 121 is a perfect square since 112=12111^2 = 121112=121, and z2z^2z2 is also a perfect square.

STEP 3

Rewrite the radical expression by separating the perfect square factors.121z2=121⋅z2\sqrt{121 z^{2}} = \sqrt{121} \cdot \sqrt{z^{2}}121z2​=121​⋅z2​

STEP 4

Take the square root of the perfect squares.Since the square root of a perfect square is the number that was squared, we have:121=11\sqrt{121} = 11121​=11 z2=z\sqrt{z^{2}} = zz2​=z

STEP 5

Multiply the results of the square roots.11⋅z=11z11 \cdot z = 11z11⋅z=11z

STEP 6

Write the simplified expression.The simplified form of 121z2\sqrt{121 z^{2}}121z2​ is 11z11z11z.Karan needs to pay $803 each month.

Start learning now

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

Simplify $\sqrt{121 z^{2}}$

Assumptions
1. We are given the radical expression $\sqrt{121 z^{2}}$ .
2. We need to simplify the expression by factoring out perfect squares from under the radical.

Identify the perfect square factors in the given expression.
The number 121 is a perfect square since $11^2 = 121$ , and $z^2$ is also a perfect square.

Rewrite the radical expression by separating the perfect square factors.
$\sqrt{121 z^{2}} = \sqrt{121} \cdot \sqrt{z^{2}}$

Take the square root of the perfect squares.
Since the square root of a perfect square is the number that was squared, we have:
$\sqrt{121} = 11$ $\sqrt{z^{2}} = z$

Multiply the results of the square roots.
$11 \cdot z = 11z$

Write the simplified expression.
The simplified form of $\sqrt{121 z^{2}}$ is $11z$ .
Karan needs to pay $803 each month.