QuestionEstimate $\sqrt{78}$ using nearby perfect squares.

Studdy Solution

STEP 1

Assumptions1. We are estimating the square root of78. We are using perfect squares to make this estimation

STEP 2

First, we need to find the perfect squares that are closest to78. The perfect square less than78 is64 (which is $8^2$ ) and the perfect square greater than78 is81 (which is $9^2$ ).

STEP 3

Now, we know that $\sqrt{78}$ is between8 and9 because $8^2 <78 <9^2$ .

STEP 4

To get a closer estimate, we can take the average of8 and9.
$Estimate = (8 +9) /2$

STEP 5

Calculate the estimate.
$Estimate = (8 +9) /2 =8.5$ The square root of78 is approximately8.5.

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QuestionEstimate $\sqrt{78}$ using nearby perfect squares.

Studdy Solution

STEP 1

Assumptions1. We are estimating the square root of78. We are using perfect squares to make this estimation

STEP 2

First, we need to find the perfect squares that are closest to78. The perfect square less than78 is64 (which is $8^2$ ) and the perfect square greater than78 is81 (which is $9^2$ ).

STEP 3

Now, we know that $\sqrt{78}$ is between8 and9 because $8^2 <78 <9^2$ .

STEP 4

To get a closer estimate, we can take the average of8 and9.
$Estimate = (8 +9) /2$

STEP 5

Calculate the estimate.
$Estimate = (8 +9) /2 =8.5$ The square root of78 is approximately8.5.

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QuestionEstimate 78\sqrt{78}78​ using nearby perfect squares.

Studdy Solution

STEP 1

Assumptions1. We are estimating the square root of78. We are using perfect squares to make this estimation

STEP 2

First, we need to find the perfect squares that are closest to78. The perfect square less than78 is64 (which is 828^282) and the perfect square greater than78 is81 (which is 929^292).

STEP 3

Now, we know that 78\sqrt{78}78​ is between8 and9 because 82<78<928^2 <78 <9^282<78<92.

STEP 4

To get a closer estimate, we can take the average of8 and9.Estimate=(8+9)/2Estimate = (8 +9) /2Estimate=(8+9)/2

STEP 5

Calculate the estimate.Estimate=(8+9)/2=8.5Estimate = (8 +9) /2 =8.5Estimate=(8+9)/2=8.5The square root of78 is approximately8.5.

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QuestionEstimate $\sqrt{78}$ using nearby perfect squares.

First, we need to find the perfect squares that are closest to78. The perfect square less than78 is64 (which is $8^2$ ) and the perfect square greater than78 is81 (which is $9^2$ ).

Now, we know that $\sqrt{78}$ is between8 and9 because $8^2 <78 <9^2$ .

To get a closer estimate, we can take the average of8 and9.
$Estimate = (8 +9) /2$

Calculate the estimate.
$Estimate = (8 +9) /2 =8.5$ The square root of78 is approximately8.5.