Solved on Nov 13, 2023

Estimate $\sqrt{15}$ to the nearest tenth, then locate it on a number line.

STEP 1

Assumptions1. We are asked to estimate $\sqrt{15}$ to the nearest tenth. . We are also asked to locate $\sqrt{15}$ on a number line.

STEP 2

First, we need to find two perfect squares that15 lies between. The perfect squares closest to15 are16 and9, which are the squares of4 and respectively.

STEP 3

Since15 is closer to16, we can say that $\sqrt{15}$ is slightly less than.

STEP 4

To estimate $\sqrt{15}$ to the nearest tenth, we can start by trying3.9. $3.9^2 =15.21$

STEP 5

Since $3.9^2$ is greater than15, we can try a smaller number. Let's try3.8.
$3.8^2 =14.44$

STEP 6

Since $3.8^2$ is less than15, and $3.9^2$ is greater than15, we can conclude that $\sqrt{15}$ is between3.8 and3.9.

STEP 7

To estimate to the nearest tenth, we can choose the one that is closer to15. Since $3.9^2$ is closer to15 than $3.^2$ , we can estimate $\sqrt{15}$ to be approximately3.9.

STEP 8

Now, to locate $\sqrt{15}$ on a number line, we need to mark the points3 and4 on the number line as $\sqrt{15}$ lies between them.

STEP 9

Then, we can mark the point slightly less than4 as $\sqrt{15}$ , since we estimated it to be3.9.
So, the estimated value of $\sqrt{15}$ is3.9 and it lies slightly less than4 on a number line.

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Estimate $\sqrt{15}$ to the nearest tenth, then locate it on a number line.

STEP 1

Assumptions1. We are asked to estimate $\sqrt{15}$ to the nearest tenth. . We are also asked to locate $\sqrt{15}$ on a number line.

STEP 2

First, we need to find two perfect squares that15 lies between. The perfect squares closest to15 are16 and9, which are the squares of4 and respectively.

STEP 3

Since15 is closer to16, we can say that $\sqrt{15}$ is slightly less than.

STEP 4

To estimate $\sqrt{15}$ to the nearest tenth, we can start by trying3.9. $3.9^2 =15.21$

STEP 5

Since $3.9^2$ is greater than15, we can try a smaller number. Let's try3.8.
$3.8^2 =14.44$

STEP 6

Since $3.8^2$ is less than15, and $3.9^2$ is greater than15, we can conclude that $\sqrt{15}$ is between3.8 and3.9.

STEP 7

To estimate to the nearest tenth, we can choose the one that is closer to15. Since $3.9^2$ is closer to15 than $3.^2$ , we can estimate $\sqrt{15}$ to be approximately3.9.

STEP 8

Now, to locate $\sqrt{15}$ on a number line, we need to mark the points3 and4 on the number line as $\sqrt{15}$ lies between them.

STEP 9

Then, we can mark the point slightly less than4 as $\sqrt{15}$ , since we estimated it to be3.9.
So, the estimated value of $\sqrt{15}$ is3.9 and it lies slightly less than4 on a number line.

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Estimate 15\sqrt{15}15​ to the nearest tenth, then locate it on a number line.

STEP 1

Assumptions1. We are asked to estimate 15\sqrt{15}15​ to the nearest tenth. . We are also asked to locate 15\sqrt{15}15​ on a number line.

STEP 2

First, we need to find two perfect squares that15 lies between. The perfect squares closest to15 are16 and9, which are the squares of4 and respectively.

STEP 3

Since15 is closer to16, we can say that 15\sqrt{15}15​ is slightly less than.

STEP 4

To estimate 15\sqrt{15}15​ to the nearest tenth, we can start by trying3.9.3.92=15.213.9^2 =15.213.92=15.21

STEP 5

Since 3.923.9^23.92 is greater than15, we can try a smaller number. Let's try3.8.3.82=14.443.8^2 =14.443.82=14.44

STEP 6

Since 3.823.8^23.82 is less than15, and 3.923.9^23.92 is greater than15, we can conclude that 15\sqrt{15}15​ is between3.8 and3.9.

STEP 7

To estimate to the nearest tenth, we can choose the one that is closer to15. Since 3.923.9^23.92 is closer to15 than 3.23.^23.2, we can estimate 15\sqrt{15}15​ to be approximately3.9.

STEP 8

Now, to locate 15\sqrt{15}15​ on a number line, we need to mark the points3 and4 on the number line as 15\sqrt{15}15​ lies between them.

STEP 9

Then, we can mark the point slightly less than4 as 15\sqrt{15}15​, since we estimated it to be3.9.So, the estimated value of 15\sqrt{15}15​ is3.9 and it lies slightly less than4 on a number line.

Start learning now

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

Estimate $\sqrt{15}$ to the nearest tenth, then locate it on a number line.

Assumptions1. We are asked to estimate $\sqrt{15}$ to the nearest tenth. . We are also asked to locate $\sqrt{15}$ on a number line.

Since15 is closer to16, we can say that $\sqrt{15}$ is slightly less than.

To estimate $\sqrt{15}$ to the nearest tenth, we can start by trying3.9. $3.9^2 =15.21$

Since $3.9^2$ is greater than15, we can try a smaller number. Let's try3.8.
$3.8^2 =14.44$

Since $3.8^2$ is less than15, and $3.9^2$ is greater than15, we can conclude that $\sqrt{15}$ is between3.8 and3.9.

To estimate to the nearest tenth, we can choose the one that is closer to15. Since $3.9^2$ is closer to15 than $3.^2$ , we can estimate $\sqrt{15}$ to be approximately3.9.

Now, to locate $\sqrt{15}$ on a number line, we need to mark the points3 and4 on the number line as $\sqrt{15}$ lies between them.

Then, we can mark the point slightly less than4 as $\sqrt{15}$ , since we estimated it to be3.9.
So, the estimated value of $\sqrt{15}$ is3.9 and it lies slightly less than4 on a number line.